Question

Find the magnitude of two vectors $\vec a \and\ \vec b$,having the same magnitude and such that the angle between them is $60^{o}$ and their scalar product is $\frac{1}{2}$.

Answer 1

As both vectors have same magnitude...

Consider x as the magnitude of the two vectors...

We know that scalar product is given by

a.b=|a||b|costheta

1/2=x.x.cos60 .....(given)

1/2=x^2 (1/2) ......(as cos60=1/2)

so we get, x^2=1

So x=1