Question

What should be the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ to get maximum magnitude of their resultant vector $\overrightarrow{R}$.

Answer 1

The angle between vector A and vector B is θθ as shown above.

The resultant is shown in red. Using the cosine rule:

$R^2=A^2+B^2-2AB\left(cos\beta \right)$

But the magnitude of each vector is the same, therefore

$A^2=A^2+A^2-2\left(A\right)\left(A\right)\left(cos\beta \right)$

$cos\beta =\frac{-A^2}{-2\left(A^2\right)}$

$\beta ={60}^o$

$\theta ={180}^o-{60}^o={60}^o$