Practice Test – VECTOR 3D Class 11 Notes | EduRev

Created by: Nimish Aren

Class 11 : Practice Test – VECTOR 3D Class 11 Notes | EduRev

 Page 1


Test – VECTOR 3D 
       
         Time :-1hr.30mins.  
Read carefully the instructions given below : 
1. The test consists of 100 marks.  
2. Q. No.1 – Q. No. 25 carries 3 marks . For every wrong answer -1 will be deducted. 
3. Q.No.26 – Q. No.30 carries 5 marks each. For every wrong answer -2 will be deducted. 
4. A student will get marks if he/she will answer all the correct choices to a problem, if more than one choice is 
the correct answer. 
 
SECTION A :- 
 
Q.1 If a line makes angles of 60° and 45° with the positive directions of the x-axis and y-axis resp. then 
the acute angle between the line and the z-axis is  
 (a) 60°    (b) 45°    (c) 75°   (d) 15° 
 
Q.2 The angle between the lines joining the points (1, 0, -3) , (2, -1, 2) and (1, 1, 1), (3, 2, 0) is 
 (a) Cos
-1
 2/9   (b) 90°    (c) 0°      (d) Cos
-1
 2v2 / 9 
 
Q.3 ABC is a triangle where A = (2, 3, 5), B = (-1, 3, 2) and C = (?, 5, µ). If the median through A is 
equally inclined with the axes then 
 (a) ? = 14, µ = 20  (b) ? = 7, µ = 10  (c) ? = 7/2, µ = 5  (d) ? = 10, µ = 7 
 
Q.4 The equation of the locus of point (1 + r/4, 1 + r/3 , 2) where r ? R, is given by 
 (a)  x – 1  =  y + 1   = z – 2  (b) x – 1  =  y + 1   = z – 2  (c) 4x – 3y = 7     (d) z = 2 
          4  3   0           3  4   0 
 
Q.5 The angle between the lines   x + 2  =  y + 3   =  z – 4     and   x – 1   =   y    =   z     is 
   1     -2         1        -1        1       0 
 (a) p / 6   (b) p / 3   (c) p / 2  (d) 0 
 
Q.6 The shortest distance between the line   x – 3   =   y   =   z    and the y-axis is 
           3         0      -4 
 (a) 1 / 5   (b) 1    (c) 0   (d) 12 / 5 
 
Q.7 The projection of the line segment joining the point (6, -2, 1) and the origin on the line   
 x – 2  =  y + 1   =  z – 1   is 
   4       – 3           0 
(a) 30    (b) 6    (c) 5   (d) none 
 
Q.8 If the sum of the reciprocals of the intercepts made by the plane ax + by + cz = 1 on the three axes is 
1 then the plane always passes through the point  
 (a) (2, -1, 0)   (b) (1, 1, 1)  (c) (-1, -1, -1)  (d) (1/2, -1, 1/2) 
 
Q.9 The direction cosines of a line parallel to the planes 3x + 4y + z = 0 and x – 2y – 3z = 5  are 
 (a) (-1, 1, -1)   (b) (-1/ v3, -1/ v3, 1/ v3) (c) (-1/ v3, 1/ v3, -1/ v3)    (d) none 
 
Q.10 If the line   x – 1  =  y + 1  =  z + 1  lies in the plane 3x – 2y + 5z = 0  then ? is  
           1            -2   ? 
 (a) 1    (b) – 7/5   (c) 5 / 7    (d) none 
 
 
Page 2


Test – VECTOR 3D 
       
         Time :-1hr.30mins.  
Read carefully the instructions given below : 
1. The test consists of 100 marks.  
2. Q. No.1 – Q. No. 25 carries 3 marks . For every wrong answer -1 will be deducted. 
3. Q.No.26 – Q. No.30 carries 5 marks each. For every wrong answer -2 will be deducted. 
4. A student will get marks if he/she will answer all the correct choices to a problem, if more than one choice is 
the correct answer. 
 
SECTION A :- 
 
Q.1 If a line makes angles of 60° and 45° with the positive directions of the x-axis and y-axis resp. then 
the acute angle between the line and the z-axis is  
 (a) 60°    (b) 45°    (c) 75°   (d) 15° 
 
Q.2 The angle between the lines joining the points (1, 0, -3) , (2, -1, 2) and (1, 1, 1), (3, 2, 0) is 
 (a) Cos
-1
 2/9   (b) 90°    (c) 0°      (d) Cos
-1
 2v2 / 9 
 
Q.3 ABC is a triangle where A = (2, 3, 5), B = (-1, 3, 2) and C = (?, 5, µ). If the median through A is 
equally inclined with the axes then 
 (a) ? = 14, µ = 20  (b) ? = 7, µ = 10  (c) ? = 7/2, µ = 5  (d) ? = 10, µ = 7 
 
Q.4 The equation of the locus of point (1 + r/4, 1 + r/3 , 2) where r ? R, is given by 
 (a)  x – 1  =  y + 1   = z – 2  (b) x – 1  =  y + 1   = z – 2  (c) 4x – 3y = 7     (d) z = 2 
          4  3   0           3  4   0 
 
Q.5 The angle between the lines   x + 2  =  y + 3   =  z – 4     and   x – 1   =   y    =   z     is 
   1     -2         1        -1        1       0 
 (a) p / 6   (b) p / 3   (c) p / 2  (d) 0 
 
Q.6 The shortest distance between the line   x – 3   =   y   =   z    and the y-axis is 
           3         0      -4 
 (a) 1 / 5   (b) 1    (c) 0   (d) 12 / 5 
 
Q.7 The projection of the line segment joining the point (6, -2, 1) and the origin on the line   
 x – 2  =  y + 1   =  z – 1   is 
   4       – 3           0 
(a) 30    (b) 6    (c) 5   (d) none 
 
Q.8 If the sum of the reciprocals of the intercepts made by the plane ax + by + cz = 1 on the three axes is 
1 then the plane always passes through the point  
 (a) (2, -1, 0)   (b) (1, 1, 1)  (c) (-1, -1, -1)  (d) (1/2, -1, 1/2) 
 
Q.9 The direction cosines of a line parallel to the planes 3x + 4y + z = 0 and x – 2y – 3z = 5  are 
 (a) (-1, 1, -1)   (b) (-1/ v3, -1/ v3, 1/ v3) (c) (-1/ v3, 1/ v3, -1/ v3)    (d) none 
 
Q.10 If the line   x – 1  =  y + 1  =  z + 1  lies in the plane 3x – 2y + 5z = 0  then ? is  
           1            -2   ? 
 (a) 1    (b) – 7/5   (c) 5 / 7    (d) none 
 
 
Q.11 The direction cosines of the normal to the plane 5(x - 2) = 3(y – z)  are 
 (a) 5, -3, 3  (b) 5/ v43, -3/ v43 , 3/ v43 (c) 1/2, -3/10, 3/10       (d) 1, -3/5, 3/5 
 
Q.12 The direction cosines of the projection of the line  x  =  y – 1  =  z + 1   on the plane  2x + y – 3z = 5  
are              -2        1           -1 
 (a) 2/3, -1/3, 2/3     (b) 2/ v14, -3/ v14, 1/ v14  
(c) 2/ v6, 1/ v6, 1/ v6     (d) 2/ v6, -1/ v6, 1/ v6 
 
Q.13 Let ABC be a triangle the position vectors of whose vertices are resp. i + 2j + 4k, -2i + 2j + k  
and 2i + 4j – 3k. Then the triangle ABC is 
(a) isosceles   (b) equilateral   (c) right angled (d) none 
 
Q.14 One of the diagonals of a parallelepiped vector is 4j – 8k. If the two diagonals of one of its faces are 
6i + 6k and 4j + 2k, then its volume is 
 (a) 60    (b) 80    (c) 100   (d) 120 
 
Q.15 If vectors a, b, c are unit vector such that  a + b – c = 0, then the angle between vector  a and b is 
 (a) p / 6   (b) p / 3   (c) p / 2  (d) 2p / 3 
 
Q.16 If vectors a, b, c are non-coplanar, then  vector  [a + 2b b + 2c c + 2a]  =  
    [a b c] 
 (a) 3    (b) 9    (c) 8   (d) 6 
 
Q.17 If  vectors a, b, c are vectors such that vector |b| = |c|, then  [(a + b) x (a + c)] x (b x c) . (b + c)  
 (a) [a b c]   (b) 0    (c) – [a b c]            (d) 2 [a b c]  
 
Q.18 If  vector |a . b| = v3 |a x b|, then the angle between vector a and b is 
 (a) p / 6   (b) p / 4   (c) p / 3  (d) p / 2 
 
Q.19 The area of the parallelogram whose diagonals are vector a – b and 3a + b, where |a| = 2, |b| = 2 and 
the angle between vector a and b is p / 6  is  
 (a) 1    (b) 4    (c) 2v3    (d) 8 
 
Q.20 If  a and b are two unit vectors then the vector (a + b) x (a x b) is parallel to the vector 
 (a) a – b   (b) a + b   (c) 2a – b  (d) 2a + b 
 
Q.21 The vector  i x (a x i) + j x (a x j) + k x (a x k) is equal to 
 (a) 0    (b) a    (c) 2a   (d) none 
 
Q.22 The volume of the tetrahedron whose vertices are the points with position vectors  i – 6j + 10k,  
-i – 3j + 7k, 5i – j + ?k and  7i – 4j + 7k  is 11 cubic units if the value of ? is 
(a) -1    (b) 1    (c) -7   (d) 7 
 
Q.23 If a, b, c are any three vectors, then  a x (b x c) = (a x b) x c if and only if 
 (a) b and c are collinear (b) a and c are collinear  (c) a and b are collinear   (d) none 
 
Q.24 The vectors AB = 3i – 2j + 2k  and BC = i – 2k are the adjacent sides of a parallelogram. An angle 
between its diagonals is 
 (a) p / 4   (b) p / 3   (c) 3p / 4  (d) 2p / 3 
 
Q.25 If  r.a  = 0, r.b = 0 and  r.c = 0 for some non-zero vectors r, then the value of [a b c] is 
 (a) 0    (b) 1 / 2   (c) 1   (d) 2 
 
Page 3


Test – VECTOR 3D 
       
         Time :-1hr.30mins.  
Read carefully the instructions given below : 
1. The test consists of 100 marks.  
2. Q. No.1 – Q. No. 25 carries 3 marks . For every wrong answer -1 will be deducted. 
3. Q.No.26 – Q. No.30 carries 5 marks each. For every wrong answer -2 will be deducted. 
4. A student will get marks if he/she will answer all the correct choices to a problem, if more than one choice is 
the correct answer. 
 
SECTION A :- 
 
Q.1 If a line makes angles of 60° and 45° with the positive directions of the x-axis and y-axis resp. then 
the acute angle between the line and the z-axis is  
 (a) 60°    (b) 45°    (c) 75°   (d) 15° 
 
Q.2 The angle between the lines joining the points (1, 0, -3) , (2, -1, 2) and (1, 1, 1), (3, 2, 0) is 
 (a) Cos
-1
 2/9   (b) 90°    (c) 0°      (d) Cos
-1
 2v2 / 9 
 
Q.3 ABC is a triangle where A = (2, 3, 5), B = (-1, 3, 2) and C = (?, 5, µ). If the median through A is 
equally inclined with the axes then 
 (a) ? = 14, µ = 20  (b) ? = 7, µ = 10  (c) ? = 7/2, µ = 5  (d) ? = 10, µ = 7 
 
Q.4 The equation of the locus of point (1 + r/4, 1 + r/3 , 2) where r ? R, is given by 
 (a)  x – 1  =  y + 1   = z – 2  (b) x – 1  =  y + 1   = z – 2  (c) 4x – 3y = 7     (d) z = 2 
          4  3   0           3  4   0 
 
Q.5 The angle between the lines   x + 2  =  y + 3   =  z – 4     and   x – 1   =   y    =   z     is 
   1     -2         1        -1        1       0 
 (a) p / 6   (b) p / 3   (c) p / 2  (d) 0 
 
Q.6 The shortest distance between the line   x – 3   =   y   =   z    and the y-axis is 
           3         0      -4 
 (a) 1 / 5   (b) 1    (c) 0   (d) 12 / 5 
 
Q.7 The projection of the line segment joining the point (6, -2, 1) and the origin on the line   
 x – 2  =  y + 1   =  z – 1   is 
   4       – 3           0 
(a) 30    (b) 6    (c) 5   (d) none 
 
Q.8 If the sum of the reciprocals of the intercepts made by the plane ax + by + cz = 1 on the three axes is 
1 then the plane always passes through the point  
 (a) (2, -1, 0)   (b) (1, 1, 1)  (c) (-1, -1, -1)  (d) (1/2, -1, 1/2) 
 
Q.9 The direction cosines of a line parallel to the planes 3x + 4y + z = 0 and x – 2y – 3z = 5  are 
 (a) (-1, 1, -1)   (b) (-1/ v3, -1/ v3, 1/ v3) (c) (-1/ v3, 1/ v3, -1/ v3)    (d) none 
 
Q.10 If the line   x – 1  =  y + 1  =  z + 1  lies in the plane 3x – 2y + 5z = 0  then ? is  
           1            -2   ? 
 (a) 1    (b) – 7/5   (c) 5 / 7    (d) none 
 
 
Q.11 The direction cosines of the normal to the plane 5(x - 2) = 3(y – z)  are 
 (a) 5, -3, 3  (b) 5/ v43, -3/ v43 , 3/ v43 (c) 1/2, -3/10, 3/10       (d) 1, -3/5, 3/5 
 
Q.12 The direction cosines of the projection of the line  x  =  y – 1  =  z + 1   on the plane  2x + y – 3z = 5  
are              -2        1           -1 
 (a) 2/3, -1/3, 2/3     (b) 2/ v14, -3/ v14, 1/ v14  
(c) 2/ v6, 1/ v6, 1/ v6     (d) 2/ v6, -1/ v6, 1/ v6 
 
Q.13 Let ABC be a triangle the position vectors of whose vertices are resp. i + 2j + 4k, -2i + 2j + k  
and 2i + 4j – 3k. Then the triangle ABC is 
(a) isosceles   (b) equilateral   (c) right angled (d) none 
 
Q.14 One of the diagonals of a parallelepiped vector is 4j – 8k. If the two diagonals of one of its faces are 
6i + 6k and 4j + 2k, then its volume is 
 (a) 60    (b) 80    (c) 100   (d) 120 
 
Q.15 If vectors a, b, c are unit vector such that  a + b – c = 0, then the angle between vector  a and b is 
 (a) p / 6   (b) p / 3   (c) p / 2  (d) 2p / 3 
 
Q.16 If vectors a, b, c are non-coplanar, then  vector  [a + 2b b + 2c c + 2a]  =  
    [a b c] 
 (a) 3    (b) 9    (c) 8   (d) 6 
 
Q.17 If  vectors a, b, c are vectors such that vector |b| = |c|, then  [(a + b) x (a + c)] x (b x c) . (b + c)  
 (a) [a b c]   (b) 0    (c) – [a b c]            (d) 2 [a b c]  
 
Q.18 If  vector |a . b| = v3 |a x b|, then the angle between vector a and b is 
 (a) p / 6   (b) p / 4   (c) p / 3  (d) p / 2 
 
Q.19 The area of the parallelogram whose diagonals are vector a – b and 3a + b, where |a| = 2, |b| = 2 and 
the angle between vector a and b is p / 6  is  
 (a) 1    (b) 4    (c) 2v3    (d) 8 
 
Q.20 If  a and b are two unit vectors then the vector (a + b) x (a x b) is parallel to the vector 
 (a) a – b   (b) a + b   (c) 2a – b  (d) 2a + b 
 
Q.21 The vector  i x (a x i) + j x (a x j) + k x (a x k) is equal to 
 (a) 0    (b) a    (c) 2a   (d) none 
 
Q.22 The volume of the tetrahedron whose vertices are the points with position vectors  i – 6j + 10k,  
-i – 3j + 7k, 5i – j + ?k and  7i – 4j + 7k  is 11 cubic units if the value of ? is 
(a) -1    (b) 1    (c) -7   (d) 7 
 
Q.23 If a, b, c are any three vectors, then  a x (b x c) = (a x b) x c if and only if 
 (a) b and c are collinear (b) a and c are collinear  (c) a and b are collinear   (d) none 
 
Q.24 The vectors AB = 3i – 2j + 2k  and BC = i – 2k are the adjacent sides of a parallelogram. An angle 
between its diagonals is 
 (a) p / 4   (b) p / 3   (c) 3p / 4  (d) 2p / 3 
 
Q.25 If  r.a  = 0, r.b = 0 and  r.c = 0 for some non-zero vectors r, then the value of [a b c] is 
 (a) 0    (b) 1 / 2   (c) 1   (d) 2 
 
Q.26 A point  Q at a distance 3 from the point  P(1, 1, 1) lying on the line joining the points  A(0, -1, 3) 
and P, has the coordinates 
 (a) (2, 3, -1)   (b) (4, 7, -5)  (c) (0, -1, 3)  (d) (-2, -5, 7) 
 
Q.27 The direction cosines of a line passing through the origin and cutting the line  x + 2 = y – 1 =  z_  
 at  Cos
-1
 v6/11  are                1          2       -1 
 (a) -1/ v11, 3/ v11, -1/ v11     (b) 1/ v11, 3/ v11, 1/ v11  
(c) -1/ v6, 2/ v6, 1/ v6      (d) -3/ v11, -1/ v11, 1/ v11 
 
Q.28 Which of the following planes intersects the planes  x – y + 2z = 3  and  4x + 3y – z = 1 along the 
same line ? 
 (a) 11x + 10y – 5z = 0  (b) 7x + 7y – 4z = 0  (c) 5x + 2y + z = 2   (d) none 
 
Q.29 Vectors perpendicular to  i – j – k  and in the plane of   i + j + k  and  -i + j + k are 
 (a) i + k   (b) 2i + j + k  (c) 3i + 2j + k  (d) – 4i – 2j – 2k 
 
Q.30 Unit vectors a, b, c are coplanar. A unit vector d is perpendicular to them. If vector (a x b) x (c x d) = 
1/6 i – 1/3 j+ 1/3 k  and the angle between a and b is 30° then vector c is 
 (a) (i – 2j + 2k) / 3      (b) (2i + j - k) / 3 
(c) (- 2i – 2j + k) / 3      (d) (- i + 2j – 2k) / 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Page 4


Test – VECTOR 3D 
       
         Time :-1hr.30mins.  
Read carefully the instructions given below : 
1. The test consists of 100 marks.  
2. Q. No.1 – Q. No. 25 carries 3 marks . For every wrong answer -1 will be deducted. 
3. Q.No.26 – Q. No.30 carries 5 marks each. For every wrong answer -2 will be deducted. 
4. A student will get marks if he/she will answer all the correct choices to a problem, if more than one choice is 
the correct answer. 
 
SECTION A :- 
 
Q.1 If a line makes angles of 60° and 45° with the positive directions of the x-axis and y-axis resp. then 
the acute angle between the line and the z-axis is  
 (a) 60°    (b) 45°    (c) 75°   (d) 15° 
 
Q.2 The angle between the lines joining the points (1, 0, -3) , (2, -1, 2) and (1, 1, 1), (3, 2, 0) is 
 (a) Cos
-1
 2/9   (b) 90°    (c) 0°      (d) Cos
-1
 2v2 / 9 
 
Q.3 ABC is a triangle where A = (2, 3, 5), B = (-1, 3, 2) and C = (?, 5, µ). If the median through A is 
equally inclined with the axes then 
 (a) ? = 14, µ = 20  (b) ? = 7, µ = 10  (c) ? = 7/2, µ = 5  (d) ? = 10, µ = 7 
 
Q.4 The equation of the locus of point (1 + r/4, 1 + r/3 , 2) where r ? R, is given by 
 (a)  x – 1  =  y + 1   = z – 2  (b) x – 1  =  y + 1   = z – 2  (c) 4x – 3y = 7     (d) z = 2 
          4  3   0           3  4   0 
 
Q.5 The angle between the lines   x + 2  =  y + 3   =  z – 4     and   x – 1   =   y    =   z     is 
   1     -2         1        -1        1       0 
 (a) p / 6   (b) p / 3   (c) p / 2  (d) 0 
 
Q.6 The shortest distance between the line   x – 3   =   y   =   z    and the y-axis is 
           3         0      -4 
 (a) 1 / 5   (b) 1    (c) 0   (d) 12 / 5 
 
Q.7 The projection of the line segment joining the point (6, -2, 1) and the origin on the line   
 x – 2  =  y + 1   =  z – 1   is 
   4       – 3           0 
(a) 30    (b) 6    (c) 5   (d) none 
 
Q.8 If the sum of the reciprocals of the intercepts made by the plane ax + by + cz = 1 on the three axes is 
1 then the plane always passes through the point  
 (a) (2, -1, 0)   (b) (1, 1, 1)  (c) (-1, -1, -1)  (d) (1/2, -1, 1/2) 
 
Q.9 The direction cosines of a line parallel to the planes 3x + 4y + z = 0 and x – 2y – 3z = 5  are 
 (a) (-1, 1, -1)   (b) (-1/ v3, -1/ v3, 1/ v3) (c) (-1/ v3, 1/ v3, -1/ v3)    (d) none 
 
Q.10 If the line   x – 1  =  y + 1  =  z + 1  lies in the plane 3x – 2y + 5z = 0  then ? is  
           1            -2   ? 
 (a) 1    (b) – 7/5   (c) 5 / 7    (d) none 
 
 
Q.11 The direction cosines of the normal to the plane 5(x - 2) = 3(y – z)  are 
 (a) 5, -3, 3  (b) 5/ v43, -3/ v43 , 3/ v43 (c) 1/2, -3/10, 3/10       (d) 1, -3/5, 3/5 
 
Q.12 The direction cosines of the projection of the line  x  =  y – 1  =  z + 1   on the plane  2x + y – 3z = 5  
are              -2        1           -1 
 (a) 2/3, -1/3, 2/3     (b) 2/ v14, -3/ v14, 1/ v14  
(c) 2/ v6, 1/ v6, 1/ v6     (d) 2/ v6, -1/ v6, 1/ v6 
 
Q.13 Let ABC be a triangle the position vectors of whose vertices are resp. i + 2j + 4k, -2i + 2j + k  
and 2i + 4j – 3k. Then the triangle ABC is 
(a) isosceles   (b) equilateral   (c) right angled (d) none 
 
Q.14 One of the diagonals of a parallelepiped vector is 4j – 8k. If the two diagonals of one of its faces are 
6i + 6k and 4j + 2k, then its volume is 
 (a) 60    (b) 80    (c) 100   (d) 120 
 
Q.15 If vectors a, b, c are unit vector such that  a + b – c = 0, then the angle between vector  a and b is 
 (a) p / 6   (b) p / 3   (c) p / 2  (d) 2p / 3 
 
Q.16 If vectors a, b, c are non-coplanar, then  vector  [a + 2b b + 2c c + 2a]  =  
    [a b c] 
 (a) 3    (b) 9    (c) 8   (d) 6 
 
Q.17 If  vectors a, b, c are vectors such that vector |b| = |c|, then  [(a + b) x (a + c)] x (b x c) . (b + c)  
 (a) [a b c]   (b) 0    (c) – [a b c]            (d) 2 [a b c]  
 
Q.18 If  vector |a . b| = v3 |a x b|, then the angle between vector a and b is 
 (a) p / 6   (b) p / 4   (c) p / 3  (d) p / 2 
 
Q.19 The area of the parallelogram whose diagonals are vector a – b and 3a + b, where |a| = 2, |b| = 2 and 
the angle between vector a and b is p / 6  is  
 (a) 1    (b) 4    (c) 2v3    (d) 8 
 
Q.20 If  a and b are two unit vectors then the vector (a + b) x (a x b) is parallel to the vector 
 (a) a – b   (b) a + b   (c) 2a – b  (d) 2a + b 
 
Q.21 The vector  i x (a x i) + j x (a x j) + k x (a x k) is equal to 
 (a) 0    (b) a    (c) 2a   (d) none 
 
Q.22 The volume of the tetrahedron whose vertices are the points with position vectors  i – 6j + 10k,  
-i – 3j + 7k, 5i – j + ?k and  7i – 4j + 7k  is 11 cubic units if the value of ? is 
(a) -1    (b) 1    (c) -7   (d) 7 
 
Q.23 If a, b, c are any three vectors, then  a x (b x c) = (a x b) x c if and only if 
 (a) b and c are collinear (b) a and c are collinear  (c) a and b are collinear   (d) none 
 
Q.24 The vectors AB = 3i – 2j + 2k  and BC = i – 2k are the adjacent sides of a parallelogram. An angle 
between its diagonals is 
 (a) p / 4   (b) p / 3   (c) 3p / 4  (d) 2p / 3 
 
Q.25 If  r.a  = 0, r.b = 0 and  r.c = 0 for some non-zero vectors r, then the value of [a b c] is 
 (a) 0    (b) 1 / 2   (c) 1   (d) 2 
 
Q.26 A point  Q at a distance 3 from the point  P(1, 1, 1) lying on the line joining the points  A(0, -1, 3) 
and P, has the coordinates 
 (a) (2, 3, -1)   (b) (4, 7, -5)  (c) (0, -1, 3)  (d) (-2, -5, 7) 
 
Q.27 The direction cosines of a line passing through the origin and cutting the line  x + 2 = y – 1 =  z_  
 at  Cos
-1
 v6/11  are                1          2       -1 
 (a) -1/ v11, 3/ v11, -1/ v11     (b) 1/ v11, 3/ v11, 1/ v11  
(c) -1/ v6, 2/ v6, 1/ v6      (d) -3/ v11, -1/ v11, 1/ v11 
 
Q.28 Which of the following planes intersects the planes  x – y + 2z = 3  and  4x + 3y – z = 1 along the 
same line ? 
 (a) 11x + 10y – 5z = 0  (b) 7x + 7y – 4z = 0  (c) 5x + 2y + z = 2   (d) none 
 
Q.29 Vectors perpendicular to  i – j – k  and in the plane of   i + j + k  and  -i + j + k are 
 (a) i + k   (b) 2i + j + k  (c) 3i + 2j + k  (d) – 4i – 2j – 2k 
 
Q.30 Unit vectors a, b, c are coplanar. A unit vector d is perpendicular to them. If vector (a x b) x (c x d) = 
1/6 i – 1/3 j+ 1/3 k  and the angle between a and b is 30° then vector c is 
 (a) (i – 2j + 2k) / 3      (b) (2i + j - k) / 3 
(c) (- 2i – 2j + k) / 3      (d) (- i + 2j – 2k) / 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Test – VECTOR 3D 
       
         Time :-1hr.30mins.  
Read carefully the instructions given below : 
5. The test consists of 100 marks.  
6. Q. No.1 – Q. No. 25 are single choice correct answer carries 3 marks . For every wrong answer -1 will be 
deducted. 
7. Q.No.26 – Q. No.30 are more than one choice as correct answer carries 5 marks each. For every wrong answer 
-2 will be deducted. 
8. Students should write the correct answer on the back of their O.R.S. 
 
 
ANSWERS 
 
SECTION A :- 
 
1.A 2.D 3.B 4.B 5.A 6.D 7.B 8.B 9.C 10.B 
11.B 12.D 13.C 14.D 15.D 16.B 17.B 18.A 19.B 20.A 
21.C 22.B,D  23.B 24.A,C  25.A 26.A,C  27.A,B,D   
28.A 29.B,D  30.A,D 
 
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