Question

If $|\vec{a}|=2,|\vec{b}|=5$ and $|\vec{a}\times \vec{b}|=8$, then $|\vec{a}\cdot \vec{b}|$ is equal to :

• A. 6
• B. 4
• C. 3
• D. 5

Answer 1

Answer: (A)

$|\vec{a}|=2,|\vec{b}|=5$
$|\vec{a}\times \vec{b}|=|\vec{a}||\vec{b}|\sin \theta =\pm 8$
$\sin \theta =\pm \frac{4}{5}\therefore \vec{a}\cdot bv=|\vec{a}||\vec{b}|\cos \theta$
$=10\cdot \left(\pm \frac{3}{5}\right)=\pm 6$
$|\vec{a}\cdot \vec{b}|=6$