( a _,^ b ) = 5 6 તથા Comp_ b a = - 2 3 તો | a | = ............ - Vidyadip

MCQ

$\left( {\overrightarrow a _,^{\overrightarrow b }} \right) = \frac{{5\pi }}{6}\ $ તથા $\ \text{Comp}_{\overrightarrow b }\overrightarrow a = - 2\sqrt 3\ $ તો $\ \left| {\overrightarrow a } \right| = \ ............$

✓
$4$
B
$6$
C
$12$
D
$4\left| {\overrightarrow b } \right|$

✓

Answer

Correct option: A.

$4$

$\text{comp}_{\overrightarrow{b}}\overrightarrow{a}= \frac {\overrightarrow{a} \cdot \overrightarrow{b}}{|\overrightarrow{b}|}$
$\therefore -2\sqrt3= \frac {|\overrightarrow{a}\|\overrightarrow{b}| \cos \theta}{|\overrightarrow{b}|}$
$\therefore -2\sqrt3=|\overrightarrow{a}|\left( -\frac {\sqrt3}{2}\right)$
$\therefore |\overrightarrow{a}| =(-2\sqrt3) \cdot\left(-\frac {2}{\sqrt3}\right)$
$\therefore |\overrightarrow{a}| =4$

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