MCQ
If $a + b + c = 0,\,\,\left| {\vec a} \right| = 3,\,\left| {\vec b} \right| = 5$ and $\left| {\vec c} \right| = 7,$ then the angle between $\vec a$ and $\vec b$ is
- ✓$\frac {\pi }{3}$
- B$\frac {\pi }{4}$
- C$\frac {\pi }{6}$
- D$\frac {\pi }{2}$
✓
Answer
Correct option: A.
$\frac {\pi }{3}$
a
$\text { Let } a+b+c=0 \Rightarrow(a+b)=-c$
$\text { Let } a+b+c=0 \Rightarrow(a+b)=-c$
$\Rightarrow \quad(a+b)^{2}=c^{2}$
$\Rightarrow a^{2}+b^{2}+2 a b=c^{2}$
$\Rightarrow 9+25+2.3 .5 \cos \theta=49$
$(\because|\vec{a}|=3,|\vec{b}|=5 \text { and }|\vec{c}|=7)$
$\therefore \cos \theta=\frac{1}{2} \Rightarrow \theta=\frac{\pi}{3}$
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