If |a b|=4,|a b|=2, then |a|^2|b|^2=

MCQ

If $|\vec{a} \times \vec{b}|=4,|\vec{a} \cdot \vec{b}|=2$, then $|\vec{a}|^2|\vec{b}|^2=$

A
$2$
✓
$20$
C
$8$
D
$6$

✓

Answer

Correct option: B.

$20$

We know that
$(\vec{a} \cdot \vec{b})^2+(\vec{a} \times \vec{b})^2=|\vec{a}|^2|\vec{b}|^2$
$|\vec{a}|^2 \cdot|\vec{b}|^2=2^2+4^4$
$|\vec{a}|^2 \cdot|\vec{b}|^2=20$

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