Question

Two vectors of the same magnitude have a resultant equal to either. What is the angle between them? (a) 50' (b) 60' (c) 75' (d) 120'

Answer 1

Answer:

The angle between the 2 vectors = Option (D) 120°

Explanation:

Let,

the 2 vectors be P and Q

and resultant of the vectors be R

Then,

$\boxed{R = \sqrt{P^{2}+Q^{2} +2PQcos\alpha } }$

In the given question,

Both vectors are equal and the resultant is also equal to them

Hence,

P = Q = R

Putting these values in we get,

$P = \sqrt{P^{2}+Q^{2} +2PQcos\alpha$

Squaring both sides we get,

$P^{2} = P^{2} +P^{2} +2P^{2}cos\alpha \\P^{2} = 2P^{2}+2P^{2}cos\alpha$

$P^{2}-2P^{2} = 2P^{2}cos\alpha \\-P^{2}=2P^{2}cos\alpha$

$cos\alpha =\frac{-1}{2}\\\alpha =120$