If $\widehat{\mathbf{u}}\ and\ \widehat{\mathbf{v}}$ unit vectors and $ heta\$is the acute angle between them, then $2\widehat{\mathbf{u}} imes 3\widehat{\mathbf{v}}$ is a unit vector for

Question

If $\widehat{\mathbf{u}}\ and\ \widehat{\mathbf{v}}$ unit vectors and $	heta\$is the acute angle between them, then $2\widehat{\mathbf{u}} 	imes 3\widehat{\mathbf{v}}$ is a unit vector for

Dr. Abubacker · Accepted Answer

(d)
Since, $\left| 2\widehat{\mathbf{u}} 	imes 3\widehat{\mathbf{v}} ight| = 1$
$\Longrightarrow 6\left| \widehat{\mathbf{u}} ight|\left| \widehat{\mathbf{v}} ight||\sin{	heta|} = 1$
$\Longrightarrow \sin{	heta = \frac{1}{6}\ \ \ \ \ \ \ \ \ \ \ \ \left\lbrack \because\left| \widehat{\mathbf{u}} ight| = \left| \widehat{\mathbf{u}} ight| = 1 ightbrack}$
Since, θ is an acute angle, then there is exactly one value of θ for which (2$\widehat{\mathbf{u}} 	imes 3\widehat{\mathbf{v}})$ is a unit vector.

Q. If $\widehat{\mathbf{u}}\ and\ \widehat{\mathbf{v}}$ unit vectors and $\theta\$is the acute angle between them, then $2\widehat{\mathbf{u}} \times 3\widehat{\mathbf{v}}$ is a unit vector for

Explanation

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