Q124 / 160 · AP EAMCET 2021 (23 Aug Shift 2) · Physics

For the resultant of two vectors $\mathbf{A}$ and $\mathbf{B}$ to maximum, the angle between them should be

  • A
    $180^{\circ}$
  • Correct answer
    B
    $0^{\circ}$
  • C
    $90^{\circ}$
  • D
    $60^{\circ}$

Solution

We know that, the magnitude of resultant of two vectors $\mathbf{A}$ and $\mathbf{B}$, $R=\sqrt{A^2+B^2+2 A B \cos \theta}$ Here, $R \rightarrow R_{\max }$, when $\cos \theta$ is maximum i.e. $\cos \theta=1$ $\theta=0^{\circ}$ Now, we get $\begin{aligned} R_{\max } & =\sqrt{A^2+B^2+2 A B} \\ & =A+B\end{aligned}$ Hence, the resultant is maximum when angle between two vectors is $0^{\circ}$.

Hence, the correct answer is option: 'B'.

Relevant Questions