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

For any vector   the value of  is equal to

Let a, b and c be distinct non-negative numbers. If the vectors  

• the Geometric Mean of a and b

• the Arithmetic Mean of a and b

• equal to zero

• equal to zero

If  are non -coplanar vector λ is a real number then

• exactly one value of λ

• no value of λ

• exactly three values of λ

• exactly three values of λ

• only y

• only x

• both x and y

• both x and y

29.

The resultant R of two forces acting on a particle is at right angles to one of them and its magnitude is one-third of the other force. The ratio of larger force to smaller one is 

• 2 : 1

• 

• 3:2

• 3:2

Let  be three non-zero vectors such that no two of these are collinear. If the vector  is collinear with is collinear with  (λ being some non-zero scalar) then  equals

• λ

• λ

• λ

• λ