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 $\bar{a}=\hat{i}+\hat{j}+\hat{k}, \bar{b}=4 \hat{i}+3 \hat{j}+4 \hat{k}$ and $\bar{c}=\hat{i}+\alpha \hat{j}+\beta \hat{k}$ are linearly dependent vectors and $|\overline{\mathrm{c}}|=\sqrt{3}$, then the values of $\alpha$ and $\beta$ are respectively.
MathematicsVector AlgebraMHT CETMHT CET 2023 (11 May Shift 2)
Options:
  • A 1,1
  • B 2,1
  • C 0,1
  • D 1,2
Solution:
2804 Upvotes Verified Answer
The correct answer is: 1,1
Note that only for option (A), i.e., for $\alpha=1$ and $\beta=1,|\vec{c}|=\sqrt{3}$ holds true.
$\therefore \quad$ Option (A) is correct.

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.