Question

If $|\overrightarrow{a}|=2,|\overrightarrow{b}|=7$ and $\overrightarrow{a}\times \overrightarrow{b}=3\hat{i}+2\hat{j}+6\hat{k},$ then $\overrightarrow{a}\cdot \overrightarrow{b}=$

• A. $\pm 11\sqrt{3}$
• B. $\pm 6\sqrt{3}$
• C. $\pm 7\sqrt{3}$
• D. $\pm 5\sqrt{3}$

Answer 1

The correct option is C $\pm 7\sqrt{3}$

We know that,
$(\overrightarrow{a}.\overrightarrow{b}{)}^2=|\overrightarrow{a}{|}^2|\overrightarrow{b}{|}^2-|\overrightarrow{a}\times \overrightarrow{b}{|}^2$
$=4\times 49-49$
$=3\times 49$
$\Rightarrow \overrightarrow{a}.\overrightarrow{b}=\pm 7\sqrt{3}$