The resultant of two vectors of same magnitude is equal to the magnitude of one of the vectors, then the angle between them is

Options

A. `30^(@)`
B. `60^(@)`
C. `90^(@)`
D. `120^(@)`

Answer

D

Explanation

We know that,
`R = sqrt(A ^(2) + B ^(2) + 2 AB cos theta)`
`A = sqrt ((A ^(2 ) + A ^(2) + 2 A ^(2) cos theta))`
`= sqrt (2 A ^(2) (1 + cos theta))`
`therefore A ^(2) = 2 A ^(2) (1 + cos theta)`
`implies cos theta =- (1)/(2)`
`implies theta = cos ^(-1) (- (1)/(2)) implies theta = 120^(@).`