Search any question & find its solution
Question:
Answered & Verified by Expert
If $|\mathbf{a} \times \mathbf{b}|=5$ and $|\mathbf{a} \cdot \mathbf{b}|=3$, then $|\mathbf{a}|^{2}|\mathbf{b}|^{2}$ is equal to
Options:
Solution:
1183 Upvotes
Verified Answer
The correct answer is:
34
We have, $|a \times b|=5$
and $|\mathbf{a} \cdot \mathbf{b}|=3$
$\because|\mathbf{a} \times \mathbf{b}|^{2}=|a|^{2}|b|^{2}-(\mathbf{a} \cdot \mathbf{b})^{2}$
$\Rightarrow \quad 25=|\mathbf{a}|^{2}|b|^{2}-9$
$\Rightarrow|\mathrm{a}|^{2}|\mathrm{~b}|^{2}=34$
and $|\mathbf{a} \cdot \mathbf{b}|=3$
$\because|\mathbf{a} \times \mathbf{b}|^{2}=|a|^{2}|b|^{2}-(\mathbf{a} \cdot \mathbf{b})^{2}$
$\Rightarrow \quad 25=|\mathbf{a}|^{2}|b|^{2}-9$
$\Rightarrow|\mathrm{a}|^{2}|\mathrm{~b}|^{2}=34$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.