MCQ
If $\vec{A}+\vec{B}=\vec{C}$ and $A = B = C$, then what should be the angle between $\vec{A}$ and $\vec{B}$ ?
- A$0$
- B$\frac{\pi}{3}$
- C$\frac{2 \pi}{3}$
- D$\pi$
✓
Answer
C. $\frac{2 \pi}{3}$
Explanation:
$
\begin{array}{l}
C=\left[A^2+B^2+2 AB \cos \frac{2 \pi}{3}\right]^{1 / 2} \\
=\left[A^2+B^2+2 A^2\left(-\frac{1}{2}\right)\right]^{1 / 2}=A=B
\end{array}
$
Explanation:
$
\begin{array}{l}
C=\left[A^2+B^2+2 AB \cos \frac{2 \pi}{3}\right]^{1 / 2} \\
=\left[A^2+B^2+2 A^2\left(-\frac{1}{2}\right)\right]^{1 / 2}=A=B
\end{array}
$
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