Let a and b be two vector such that |a|=14, |b|=6 and |a b|=48. T… - Vidyadip

MCQ

Let $\vec{a}$ and $\vec{b}$ be two vector such that $|\vec{a}|=\sqrt{14}$, $|\vec{b}|=\sqrt{6}$ and $|\vec{a} \times \vec{b}|=\sqrt{48}$. Then $(\vec{a} \cdot \vec{b})^2$ is equal to $...........$.

✓
$36$
B
$35$
C
$37$
D
$39$

✓

Answer

Correct option: A.

$36$

a
$|\vec{a}|=\sqrt{14},|\vec{b}|=\sqrt{6} \quad|\vec{a} \times \vec{b}|=\sqrt{48}$

$|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=|\vec{a}|^2 \times|\vec{b}|^2$

$\Rightarrow(\vec{a} \cdot \vec{b})^2=84-48=36$

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