If a + b + c = 0, , , | a | = 3, , | b | = 5 and | c | = 7, then the angle between a and b is

If a + b + c = 0, , , | a | = 3, , | b | = 5 and | c

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
$\text { Let } a+b+c=0 \Rightarrow(a+b)=-c$

$\Rightarrow \quad(a+b)^{2}=c^{2}$

$\Rightarrow a^{2}+b^{2}+2 a b=c^{2}$

$\Rightarrow 9+25+2.3 .5 \cos \theta=49$

$(\because|\vec{a}|=3,|\vec{b}|=5 \text { and }|\vec{c}|=7)$

$\therefore \cos \theta=\frac{1}{2} \Rightarrow \theta=\frac{\pi}{3}$

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