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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
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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