Question

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

Answer 1

The correct answer is: $⇒|\vec{a}|=|\vec{b}|=1$
Let $θ$ be the angle between the vectors $\vec{a}$ and $\vec{b}$.
It is given that $|\vec{a}|=|\vec{b}|,\vec{a}.\vec{b}=\frac{1}{2},and\, θ =60°...(1)$
We know that $\vec{a}.\vec{b}=|\vec{a}||\vec{b}|cosθ$
$∴\frac{1}{2}=|\vec{a}||\vec{a}|cos60° [using(1)]$
$⇒\frac{1}{2}=|\vec{a}|^2\times\frac{1}{2}$
$⇒|\vec{a}|^2=1$
$⇒|\vec{a}|=|\vec{b}|=1$