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Multiplication with Vectors

If A⃗·B⃗=|A⃗×...

Question

If $\to A . \to B = | \to A \times \to B |,$ find angle between $\to A$ and $\to B .$

A

45^{\circ}

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B

35^{\circ}

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C

54^{\circ}

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D

72^{\circ}

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Solution

The correct option is A $45^{\circ}$
$\to A . \to B = | \to A \times \to B |,$
$A B cos θ = A B sin θ$
$tan θ = 1$
$\Rightarrow θ = 45^{\circ}$

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