The angle between two vector A and B is `theta`. Vector R is the resultant of the two vectors. If R makes an angle `(theta)/(2)` with A, then

Options

A. `A=2B`
B. `A=B//2`
C. `A=B`
D. `AB=1`

Answer

C

Explanation

Graphically:
`/_ROQ=theta//2, /_RQO=theta//2`
Hence, `DeltaOQR` is isosceles.
`rArr OR= RQrArr B=A`
Analytically:
`tan(theta//2) =(Bsin theta)/(A+B cos theta)`
`rArr (sin(theta//2))/(cos(theta//2))=(2Bsin(theta//2) cos(theta//2))/(A+B[2cos^(2)(theta//2)-1])` ltbr `rArr A+2 Bcos^(2)(theta//2)-B=2B cos^(2)(theta//2)rArr A=B`
` rArr A+2B cos^(2)(theta//2)-B=2B cos^(2)(theta//2) rArr A=B`