Let a, b, c three unit vectors such that a ^ .b ^ + b ^ .c ^ - a … - Vidyadip

MCQ

Let $\vec a, \vec b, \vec c$ three unit vectors such that $\mathop a\limits^ \to \mathop {.b}\limits^ \to + \mathop b\limits^ \to \mathop {.c}\limits^ \to - \mathop a\limits^ \to \mathop {.c}\limits^ \to = \frac{3}{2}$ Then the value of $\mathop a\limits^ \to \mathop {.b}\limits^ \to + \mathop b\limits^ \to \mathop {.c}\limits^ \to + \mathop c\limits^ \to \mathop {.a}\limits^ \to $

✓
$\frac{1}{2}$
B
$1$
C
$\frac{3}{2}$
D
$-\frac{1}{2}$

✓

Answer

Correct option: A.

$\frac{1}{2}$

a
$\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}-\vec{a} \cdot \vec{c}=\frac{3}{2}$

$\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}}=\frac{3}{2}+2 \cdot \overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}}$

$=\frac{3}{2}+2 \times \cos 120^{\circ}=1$

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