Vector Algebra Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. If  are three non-coplanar non-zero vectors, then 
 is equal to
(a)
(b)
(c)
(d) None of these
2. If , , and   are linearly
dependent vectors and ,  then
(a)
(b)
(c)
(d)
3. If  and  are any two non-collinear mutually perpendicular unit
vectors and  is any vector, then
Page 2


PART-I (Single Correct MCQs)
1. If  are three non-coplanar non-zero vectors, then 
 is equal to
(a)
(b)
(c)
(d) None of these
2. If , , and   are linearly
dependent vectors and ,  then
(a)
(b)
(c)
(d)
3. If  and  are any two non-collinear mutually perpendicular unit
vectors and  is any vector, then
 is equal to :
(a)
(b)
(c)
(d) None
4. The values of a for which the vector  makes an
obtuse angle with the z-axis and the vectors
and
are mutually orthogonal are
(a)
(b)
(c)
(d)
5. If ,  and  are the position vectors of
the vertices A, B and C respectively of triangle ABC. The position
vector of the point where the bisector of angle A meets BC is :
(a)
(b)
(c)
(d)
Page 3


PART-I (Single Correct MCQs)
1. If  are three non-coplanar non-zero vectors, then 
 is equal to
(a)
(b)
(c)
(d) None of these
2. If , , and   are linearly
dependent vectors and ,  then
(a)
(b)
(c)
(d)
3. If  and  are any two non-collinear mutually perpendicular unit
vectors and  is any vector, then
 is equal to :
(a)
(b)
(c)
(d) None
4. The values of a for which the vector  makes an
obtuse angle with the z-axis and the vectors
and
are mutually orthogonal are
(a)
(b)
(c)
(d)
5. If ,  and  are the position vectors of
the vertices A, B and C respectively of triangle ABC. The position
vector of the point where the bisector of angle A meets BC is :
(a)
(b)
(c)
(d)
6. Let, ,   & 
 be three non-zero vectors such that  is a unit
vector perpendicular to both . If the angle between  is ,
then  is equal to
(a) 0
(b) 1
(c)
(d)
7. The vector  lies in the plane of the vectors 
and  and bisects the angle between  and . Then  which one
of the following gives possible values of a and ß?
(a) a = 2,  ß = 2
(b) a = 1,  ß = 2
(c) a = 2,  ß = 1
(d) a = 1,  ß = 1
8. Let  be three mutually perpendicular vectors of the same
magnitude. If a vector  satisfies the equation
 =  then  is given by
(a)
(b)
Page 4


PART-I (Single Correct MCQs)
1. If  are three non-coplanar non-zero vectors, then 
 is equal to
(a)
(b)
(c)
(d) None of these
2. If , , and   are linearly
dependent vectors and ,  then
(a)
(b)
(c)
(d)
3. If  and  are any two non-collinear mutually perpendicular unit
vectors and  is any vector, then
 is equal to :
(a)
(b)
(c)
(d) None
4. The values of a for which the vector  makes an
obtuse angle with the z-axis and the vectors
and
are mutually orthogonal are
(a)
(b)
(c)
(d)
5. If ,  and  are the position vectors of
the vertices A, B and C respectively of triangle ABC. The position
vector of the point where the bisector of angle A meets BC is :
(a)
(b)
(c)
(d)
6. Let, ,   & 
 be three non-zero vectors such that  is a unit
vector perpendicular to both . If the angle between  is ,
then  is equal to
(a) 0
(b) 1
(c)
(d)
7. The vector  lies in the plane of the vectors 
and  and bisects the angle between  and . Then  which one
of the following gives possible values of a and ß?
(a) a = 2,  ß = 2
(b) a = 1,  ß = 2
(c) a = 2,  ß = 1
(d) a = 1,  ß = 1
8. Let  be three mutually perpendicular vectors of the same
magnitude. If a vector  satisfies the equation
 =  then  is given by
(a)
(b)
(c)
(d)
9. Let  be non-coplanar unit vectors equally inclined to one
another at an acute angle ?. Then  in terms of ? is equal to
(a)
(b)
(c)
(d) None of these
10. If the p
th
, q
th
 and r
th
 terms of a G.P. are positive numbers a, b and c
respectively, then find the angle between the vectors
 and
(a)
(b)
(c)
(d)
11. Force  and  are acting at the point P (0,
1, 2). The moment of these forces about the point A (1, – 2, 0) is
(a)
(b)
(c)
(d) None of these
12. If  and  are non-collinear vectors, then the value of a for which the
Page 5


PART-I (Single Correct MCQs)
1. If  are three non-coplanar non-zero vectors, then 
 is equal to
(a)
(b)
(c)
(d) None of these
2. If , , and   are linearly
dependent vectors and ,  then
(a)
(b)
(c)
(d)
3. If  and  are any two non-collinear mutually perpendicular unit
vectors and  is any vector, then
 is equal to :
(a)
(b)
(c)
(d) None
4. The values of a for which the vector  makes an
obtuse angle with the z-axis and the vectors
and
are mutually orthogonal are
(a)
(b)
(c)
(d)
5. If ,  and  are the position vectors of
the vertices A, B and C respectively of triangle ABC. The position
vector of the point where the bisector of angle A meets BC is :
(a)
(b)
(c)
(d)
6. Let, ,   & 
 be three non-zero vectors such that  is a unit
vector perpendicular to both . If the angle between  is ,
then  is equal to
(a) 0
(b) 1
(c)
(d)
7. The vector  lies in the plane of the vectors 
and  and bisects the angle between  and . Then  which one
of the following gives possible values of a and ß?
(a) a = 2,  ß = 2
(b) a = 1,  ß = 2
(c) a = 2,  ß = 1
(d) a = 1,  ß = 1
8. Let  be three mutually perpendicular vectors of the same
magnitude. If a vector  satisfies the equation
 =  then  is given by
(a)
(b)
(c)
(d)
9. Let  be non-coplanar unit vectors equally inclined to one
another at an acute angle ?. Then  in terms of ? is equal to
(a)
(b)
(c)
(d) None of these
10. If the p
th
, q
th
 and r
th
 terms of a G.P. are positive numbers a, b and c
respectively, then find the angle between the vectors
 and
(a)
(b)
(c)
(d)
11. Force  and  are acting at the point P (0,
1, 2). The moment of these forces about the point A (1, – 2, 0) is
(a)
(b)
(c)
(d) None of these
12. If  and  are non-collinear vectors, then the value of a for which the
vectors  and  are collinear is :
(a)
(b)
(c) –
(d) –
13. If  and ,
, then what is the value of ?
(a)
(b)
(c)
(d)
14. The points D, E, F divide BC, CA and AB of the triangle ABC in the
ratio 1 : 4, 3 : 2 and 3 : 7 respectively and the point K divides AB in the
ratio 1 : 3, then  is equal to
(a) 1 : 1
(b) 2 : 5
(c) 5 : 2
(d) None of these
15. Let ,  and . The vector 
which satisfies the equations