First slide

Vectors

Question

$| \vec{A} \times \vec{B} |^{2} + | \vec{A} . \vec{B} |^{2} =$

Moderate

A

zero
B

$A^{2} B^{2}$
C

AB
D

$\sqrt{AB}$

Solution

Let $θ$ be angle between vectors $\vec{A} and \vec{B}$
$∴ | \vec{A} \times \vec{B} | = ABsinθ$
and $| \vec{A} . \vec{B} | = ABcosθ$
$| \vec{A} \times \vec{B} |^{2} = | \vec{A .} \vec{B} |^{2} = {(ABsinθ)}^{2} + {(ABcosθ)}^{2}$
= $A^{2} B^{2} \sin^{2} θ + A^{2} B^{2} \cos^{2} θ = A^{2} B^{2}$

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