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 xaxis and yaxis resp. then the acute angle between the line and the zaxis 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 yaxis 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 xaxis and yaxis resp. then the acute angle between the line and the zaxis 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 yaxis 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 noncoplanar, 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 nonzero 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 xaxis and yaxis resp. then the acute angle between the line and the zaxis 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 yaxis 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 noncoplanar, 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 nonzero 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 xaxis and yaxis resp. then the acute angle between the line and the zaxis 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 yaxis 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 noncoplanar, 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 nonzero 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,DRead More
Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 