Search any question & find its solution
Question:
Answered & Verified by Expert
If $\vec{a}$ and $\vec{b}$ are two vectors such that $|\vec{a}|=|\vec{b}|=\sqrt{14}$ and $\vec{a} \cdot \vec{b}=-7$, then $\frac{|\vec{a} \times \vec{b}|}{|\vec{a} \cdot \vec{b}|}=$
Options:
Solution:
2807 Upvotes
Verified Answer
The correct answer is:
$\sqrt{3}$
Given, $\vec{a} \cdot \vec{b}=-7 \Rightarrow|\vec{a}||\vec{b}| \cos \theta=7$
$\Rightarrow \cos \theta=\frac{1}{2} \Rightarrow \tan \theta=\sqrt{3}$
Now, $\frac{|\vec{a} \times \vec{b}|}{|\vec{a} \cdot \vec{b}|}=\frac{|\vec{a}||\vec{b}| \sin \theta}{|\vec{a}||\vec{b}| \cos \theta}=\tan \theta=\sqrt{3}$
$\Rightarrow \cos \theta=\frac{1}{2} \Rightarrow \tan \theta=\sqrt{3}$
Now, $\frac{|\vec{a} \times \vec{b}|}{|\vec{a} \cdot \vec{b}|}=\frac{|\vec{a}||\vec{b}| \sin \theta}{|\vec{a}||\vec{b}| \cos \theta}=\tan \theta=\sqrt{3}$
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.