Under which condition will the magnitude of the resultant of two vectors be equal to that of any one of the constituent vectors ?

Explanation

Suppose, a and b are the magnitudes of two vectors and the angle between them is `theta` . According to the problem let the magnitude of the resultant of `veca and vecb` be equal to a . Therefore,
`a^2=a^2+b^2+2abcos theta or, b(b+2a cos theta)=0`
`therefore b+2acos theta=0[because b ne0]`
or, `theta = cos^(-1)(-b/(2a))`
that is , if the angle between `veca and vecb` is =`cos^(-1)(-b/(2a)) or cos^(-1)(-a/(2b))`, the magnitude of the resultant vector is equal to a or b respectively.