Question

If  are unit vectors and θ is the acute angle between them, then  is a unit vector for

Solution

Correct option is

Exactly one value of θ

 

It is given that  = 1 and θ is the acute angle between   

  

Now,

          

          

  

As θ is an acute angle. So, there is only one value of θ for which  is a unit vector. 

SIMILAR QUESTIONS

Q1

If , then the value of  is equal to

Q2

Angle between vectors  are unit vectors satisfying 

Q3

The values of ‘a’ for which the points ABC with position vectors  respectively are the vertices of a right angled triangle with C = π/2 are 

Q4

The vectors  are the adjacent sides of a parallelogram. Then, the acute angle between its diagonals is

Q5

If  are two vectors such that  then angle between 

Q6

The values of x for which the angle between the vectors  is acute, and the angle between the vector  and the axis of ordinates is obtuse, are

Q7

The value of x for which the angle between  and  is obtuse and the angle between  and the z-axis is acute and less than π/6, are  

Q8

If  are two unit vectors such that , then the angle between , is 

Q9

, then the angle between