Vector Algebra: Mathematics MCQ

 

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Q.1. The vector   lies in the plane of the vectors  and bisect the angle between  . Then which one of the following gives possible values of     (AIEEE 2008) 

A) 

B) 

C) 

D)  

Q2. If 4i+7j+8k, 2i+3j+4k and 2i+5j+7k are the position vectors of the vertices A,B and C respectively of triangle ABC. The position vectors of the point where the bisectors of angle A meets BC is... (Pb. CET 2004)

A) 

B) 

C) 

D)  

Q.3. Direction of a reciprocal vector of a vector  is    ( MP PET 2013)

a) Same as that of 

B) Opposite to 

C) Perpendicular to 

D) None of these

Q.4. If  , then 

A) 6

B) 7

C) 9

D) 10

Explanation-

             

Q.5. If the position vector of three points are  then the three points are 

A) Collinear 

B) Non-coplanar

C) Non-collinear

D) Non of these 

Explanation-

Let P,Q, R be the given points. Then, we have 

                   QR=-2PQ

Hence, P,Q and R are collinear.

Q.6. If the vectors  are collinear then find the value of  

A) 4

B) 6

C) 8

D) 10

Explanation-

 

Q.7. If the origin is the centroid of the triangle whose vertices are A (a, 2, -1) , B (5, b, 2) and C (-3, 1, (C) then find the values of a , b and c .

A) a = 2 , b = 3 , c = 1

B) a = 1 , b = 2 , c = 3

C) a = - 2 , b = - 3 , c = 1

D) a = 2 , b = 3 , c = 1

Explanation-

 

Q.8. If O be the origin and the position vector of A be 4 i +5 j , then a unit vector parallel to  is

A) 

B) 

C) 

D)  

Explanation-

 

Q.9. If  then find  

A) 8

B) 10

C) 14

D) 20

Explanation-

We have, 

 

Q.10. Find the vector of magnitude 3 units which is parallel to  .

A) 2/5 ()

B) 3/5()

C) 7/5()

D) 3/5()

Explanation-