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Multiplication with Vectors

The magnitude...

Question

The magnitude of the vector product of two vectors is $\sqrt{3}$ times the scalar product.The angle between vector is:

A

\frac{π}{4}

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B

\frac{π}{6}

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C

\frac{π}{3}

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D

\frac{π}{2}

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Solution

The correct option is C $\frac{π}{3}$
According to the question,
$| \to A \times \to B | = \sqrt{3} | \to A . \to B |$
Expanding the vector and the dot products:
$A B s i n θ = \sqrt{3} A B c o s θ$

$\Rightarrow t a n θ = \sqrt{3}$
$\Rightarrow θ = 60^{\circ} = \frac{π}{3}$

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