Question

If $|a|=2,|\overline{b}|=5$ and $|(\overline{a}\times \overline{b})|=8$, then the value of $\overline{a}.\overline{b}$ is:

• A. $4$
• B. $6$
• C. $8$
• D. $10$

Answer 1

The correct option is B $6$

We have his formula, $|\overline{a}.\overline{b}{|}^2=|\overline{a}{|}^2|\overline{b}{|}^2-|\overline{a}\times \overline{b}{|}^2$
$\therefore |\overline{a}.\overline{b}{|}^2=2^2\times 5^2-8^2$
$=100-64=36$
$\Rightarrow |\overline{a}.\overline{b}|=6$