Question

If $|a\times b|=4and|a.b|=2,then{\left|a\right|}^2{\left|b\right|}^2$ is equal to

• A. $2$
• B. $6$
• C. $8$
• D. $20$

Answer 1

The correct option is D $20$

$|a\times b|=\left|a\right|\left|b\right|sin\theta =4$ , also, $|a,b|=\left|a\right|\left|b\right|cos\theta =2$

Squaring and adding a both, we get

${\left|a\right|}^2{\left|b\right|}^{2}si{n}^2\theta +{\left|a\right|}^2+{\left|b\right|}^{2}co{s}^2\theta =16+4=20$

${\left|a\right|}^2{\left|b\right|}^2(si{n}^2\theta +co{s}^2\theta )=20$

${\left|a\right|}^2{\left|b\right|}^2=20$

Option (D) is correct