Let the vectors a ; and b be such that | a | = 3 ; and ; | b | = … - Vidyadip

Question

Let the vectors $\vec a\;$ and $\vec b$ be such that $\left| {\vec a} \right| = 3\;$ and $\;\left| b \right| = \frac{{\sqrt 2 }}{3},\;$ then $\;\vec a \times \vec b$ is a unit vector if the angle between $\vec a\;$ and $\vec b\;$ is

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Answer

It is given that $\overrightarrow{a}\times \overrightarrow{b}$ is a unit vector, then:
$\Rightarrow |\vec a\times \vec b|=1\Rightarrow |\vec a||\vec b|sin\theta =1$
$\Rightarrow 3.\frac{\sqrt2}{3}sin\theta=1\Rightarrow sin\theta =\frac{1}{\sqrt2}\Rightarrow \theta =\frac{\pi}{4}$

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