Question

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are vectors such that $\left|\overrightarrow{a}\right|=2,\left|\overrightarrow{b}\right|=7$ and $\overrightarrow{a}\times \overrightarrow{b}=3\hat{i}+2\hat{j}+6\hat{k}$, then what is the acute angle between $\overrightarrow{a}$ and $\overrightarrow{b}$?

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

Answer: (A)

${30}^o$

we know that,

$|a$ x $b|=|a||b|sin\theta \Rightarrow sin\theta =\frac{|a\times b|}{|a||b|}=\frac{\sqrt{9+4+36}}{7\ast 2}=\frac{7}{14}=\frac{1}{2}$

since, $sin\theta =\frac{1}{2}\Rightarrow \theta ={30}^o$

Therefore, Answer is $A$