Question

If $|\vec{a}|=2,|\vec{b}|=5$ and $|\vec{a}\times b|=8,$ then $\vec{a}\cdot \vec{b}$ = ?

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

Answer: (D)

Given, $|a|=2,|b|=5$
$\because$ $a\times b=|a||b|\sin \theta .n$
$\Rightarrow$ $|a\times b|=|a||b|\sin \theta .1$
$(\because |n|=1)$
$\Rightarrow$ $8=2\times 5.\sin \theta$
$[\because |a\times b|=8(given)]$
$\Rightarrow$ $\sin \theta =\frac{4}{5}$
$\therefore$ $\cos \theta =\sqrt{1-{\left(\frac{4}{5}\right)}^2}=\sqrt{\frac{9}{25}}=\frac{3}{5}$
Now, $a.b=|a||b|cos\theta$
$\Rightarrow$ $a.b=2\times 5\times \frac{3}{5}=6$