Search any question & find its solution
Question:
Answered & Verified by Expert
If the magnitude of $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}$ equals to $\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}$, then which one of the following is correct?
Options:
Solution:
2416 Upvotes
Verified Answer
The correct answer is:
The angle between $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ is $45^{\circ}$
Since magnitude of $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}=$ magnitude of $\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}$
$\therefore|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|=|\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}|$
$\Rightarrow|\vec{a}||\vec{b}| \sin \theta=|\vec{a}||\vec{b}| \cos \theta$ (By Definition)
$\Rightarrow \tan \theta=1$
$\Rightarrow \theta=\frac{\pi}{4}$
$\therefore|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|=|\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}|$
$\Rightarrow|\vec{a}||\vec{b}| \sin \theta=|\vec{a}||\vec{b}| \cos \theta$ (By Definition)
$\Rightarrow \tan \theta=1$
$\Rightarrow \theta=\frac{\pi}{4}$
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.