Given that `P= Q = R`. If `vecP + vecQ = vecR` then the angle between `vecP & vecR` is `theta_1`. If `vecP + vecQ + vecR=vec0` then the angle between `vecP& vecR ` is `theta_2`. What is the relation between `theta_1 and theta_2` ?

Options

A. `theta_(1)=theta_(2)`
B. `theta_(1)=(theta_(2))/(2)`
C. `theta_(1)=2theta_(2)`
D. None of the above

Answer

B

Explanation

Since `P=Q=R`

Therefore triangle formed by vectors `vecP, vecQ and vecR` will be equilateral triangle.
Now if `vecP+vecQ=vecR`, then `vecP & vecQ` will be in same order and `vecR` will be in their reverse order.
From the diagram, angle between `vecP & vecR=theta=60^(@)`
But if `vecP+vecQ+vecR=vec0` then `vecP, vecQ & vecR` will be in same order
From the diagram, angle between
`vecP & vecR=theta_(2)=180^(@)-60^(@)=120^(@)`

`(theta_(1))/(theta_(2))=(60^(@))/(120^(@))=(1)/(2) rArr theta_(1)=(theta_(2))/(2)`