Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If $|\vec{a}|=2,|\vec{b}|=5$ and $|\vec{a} \times \vec{b}|$, then what is $\vec{a} \cdot \vec{b}$ equal to ?
MathematicsVector AlgebraNDANDA 2014 (Phase 2)
Options:
  • A 6
  • B 7
  • C 8
  • D 9
Solution:
2513 Upvotes Verified Answer
The correct answer is: 6
Given $|\mathrm{a}|=2,|\mathrm{~b}|=5$ and $|\mathrm{a} \times \mathrm{b}|=8$
Also $|\mathrm{a} \times \mathrm{b}|=|\mathrm{a}| \cdot|\mathrm{b}| \cdot|\sin \theta|$
$\Rightarrow|\sin \theta|=\frac{8}{2 \times 5}=\frac{4}{5}$
$\Rightarrow|\cos \theta|=\frac{3}{5} \Rightarrow \cos \theta=\pm \frac{3}{5}$
$\therefore \mathrm{a} \cdot \mathrm{b}=|\mathrm{a}| \cdot|\mathrm{b}| \cos \theta=2 \times 5 \times \frac{3}{5}=6$

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.