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

• Exactly two values of θ

• More than two values of θ

• No value of θ

• No value of θ

A particle just clears a wall of height b at a distance a and strikes the ground at a distance c from the point of projection. The angle of projection is-

• 

• 45°

• 
• 

• 0

• -1

• -2

• -2

ABC is a triangle, right angled at A. The resultant of the forces acting along  respectively is the force along  where D is the foot of the perpendicular from A onto BC. The magnitude of the resultant is

• inclined at an angle of π/3 between them

• inclined at an angle of π/6 between them

• perpendicular

• perpendicular

A particle has two velocities of equal magnitude inclined to each other at an angle θ. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then θ is

• 90°

• 120°

• 45°

• 45°

The values of a, for which the points A, B, C with position vectors respectively are the vertices of a right-angled triangle with C =π/2  are

• 2 and 1

• −2 and −1

• −2 and 1

• −2 and 1

ABC is a triangle. Forces  acting along IA, IB and IC respectively are in equilibrium, where I is incentre of ∆ABC. Then P : Q : R is

• sin A : sin B : sin C

• 
• 
• 

If C is the mid -point of AB and P is any point outside AB, then

370.

For any vector   the value of  is equal to

• 
• 
• 
•