Can the magnitude of the resultant of two equal vectors be equal to the magnitude of each of the vectors ? Explain .

Explanation

Let the mangniture of each vector and of the resultant be a and the angle between the vectors be `alpha`.
Hence, `a^2=a^2+a^2+2a*a cos alpha`
or,` a^2=2a^2(1+cos alpha) or, 2(1+cos alpha)=1`
or, `cos alpha =1/2 -1=-1/2= cos 120 ^@`
`therefore alpha =120^@`
Hence, the magnitude to the resultant of two equal vectors is equal to that of each of the given vectors when they are inclined at an angle of `120^@` with each other.