Q148 / 160 · WBJEE 2010 · Physics

If $\vec{a}+\vec{b}=\vec{c}$ and $a+b=c$, then the angle included between $\vec{a}$ and $\vec{b}$ is

  • A
    $90^{\circ}$
  • B
    $180^{\circ}$
  • C
    $120^{\circ}$
  • Correct answer
    D
    Zero

Solution

Hints: Here $\vec{a}+\vec{b}=\vec{c} \& c=a+b$ Now, $c=\sqrt{a^2+b^2+2 a b \cos \theta}$ $\begin{aligned} & (a+b)=\sqrt{a^2+b^2+2 a b \cos \theta} \\ & a^2+b^2+2 a b=a^2+b^2+2 a b \cos \theta \\ & \cos \theta=1, \theta=0^{\circ} \end{aligned}$

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

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