If a, b and c are unit vectors such that a is perpendicular to b … - Vidyadip

MCQ

If $\vec a,\vec b$ and $\vec c$ are unit vectors such that $\vec a$ is perpendicular to $\vec b$ and $\vec c$ and $\left| {\vec a + \vec b + \vec c} \right| = 1$ , then angle between $\vec b$ and $\vec c$ is

✓
$\pi $
B
$\frac{\pi }{2}$
C
$0$
D
$\frac{{2\pi }}{3}$

✓

Answer

Correct option: A.

$\pi $

a
$\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=0$ and $\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}=0$

$|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}|^{2}=1+1+1+2(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}})=1$

$\Rightarrow \quad \overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}}=-1 \Rightarrow \overrightarrow{\mathrm{c}} \wedge \overrightarrow{\mathrm{a}}=\pi$

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