Search any question & find its solution
Question:
Answered & Verified by Expert
If $|\mathbf{a}|=2,|\mathbf{b}|=5$ and $|\mathbf{a} \times \mathbf{b}|=8$, then $\mathbf{a} \cdot \mathbf{b}$ is equal to
Options:
Solution:
2512 Upvotes
Verified Answer
The correct answer is:
6
$\begin{aligned}
& \mathbf{a} \cdot \mathbf{b}=|\mathbf{a}||\mathbf{b}| \cos \theta ; B u t \\
& \Rightarrow \sin \theta=\frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{a}||\mathbf{b}|}=\frac{4}{5} \Rightarrow \cos \theta=\frac{3}{5} \\
& \text {Therefore, } \\
& \mathbf{a} \cdot \mathbf{b}=2 \times 5 \times \frac{3}{5}=6
\end{aligned}$
& \mathbf{a} \cdot \mathbf{b}=|\mathbf{a}||\mathbf{b}| \cos \theta ; B u t \\
& \Rightarrow \sin \theta=\frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{a}||\mathbf{b}|}=\frac{4}{5} \Rightarrow \cos \theta=\frac{3}{5} \\
& \text {Therefore, } \\
& \mathbf{a} \cdot \mathbf{b}=2 \times 5 \times \frac{3}{5}=6
\end{aligned}$
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.