Vector Algebra - Online Test

Q1. The scalar product of two nonzero vectors  is defined as
Answer : Option B
Explaination / Solution:

The scalar product of two nonzero vectors  is defined as : 

Q2.
Answer : Option D
Explaination / Solution:



Q3. If θ is the angle between vectors   then the cross product 
Answer : Option D
Explaination / Solution:

If  is the angle between vectors  then, the cross product : 
 .

Q4. Find the unit vector in the direction of the vector 
Answer : Option C
Explaination / Solution:



Q5. If a is a non zero vector of magnitude ‘a’ and  a non zero scalar, then    is a unit vector if
Answer : Option B
Explaination / Solution:

   is a unit vector if and only if a is equal to .

Q6.
Answer : Option C
Explaination / Solution:



Q7. Find a unit vector perpendicular to each of  where 
Answer : Option D
Explaination / Solution:

It is given that:

Therefore, the unit vector perpendicular to both the vectors 
and
 is given by:

Q8. If a unit vector  makes angles , then find 
Answer : Option C
Explaination / Solution:

Let

It is given that   

, then,

Putting these values in (1), we get:


Q9. If a unit vector a makes angles , then the components of a are
Answer : Option D
Explaination / Solution:

Let,, then ,

Putting these values in (1) , we get :


Q10.

If θ is the angle between two vectors  then  only when

Answer : Option D
Explaination / Solution: