If u and v are unit vectors and is the acute angle between them, … - Vidyadip

MCQ

If $\vec u$ and $\vec v$ are unit vectors and $\theta$ is the acute angle between them, then $2 \vec u \times 3 \vec v$ is a unit vector for

✓
exactly one value of $\theta$
B
exactly two value of $\theta$
C
more than two values of $\theta$
D
no value of $\theta$

✓

Answer

Correct option: A.

exactly one value of $\theta$

a
Given $|2 \widehat{u} \times 3 \hat{v}|=1$

and $\theta$ is acute angle between $\widehat{u}$

and $\hat{v},|\widehat{u}|=1,|\hat{v}|=1$

$\Rightarrow \quad 6|\widehat{u}||\hat{v}||\sin \theta|=1$

$\Rightarrow 6|\sin \theta|=1 \Rightarrow \sin \theta=\frac{1}{6}$

Hence, there is exactly one value of $\theta$

for which $2 \widehat{u} \times 3 \hat{v}$ is a unit vector

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