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Question: Answered & Verified by Expert
The unit vector perpendicular to the vectors $6 \hat{i}+2 \hat{j}+3 \hat{k}$ and $3 \hat{i}-6 \hat{j}-2 \hat{k}$ is $-$
MathematicsVector AlgebraJEE Main
Options:
  • A $\frac{2 \hat{i}-3 \hat{j}+6 \hat{k}}{7}$
  • B $\frac{2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}}{7}$
  • C $\frac{2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}}{7}$
  • D $\frac{2 \hat{i}+3 \hat{j}+6 \hat{k}}{7}$
Solution:
1907 Upvotes Verified Answer
The correct answer is: $\frac{2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}}{7}$
Unit vector perpendicular to both the given vectors is, $\frac{(6 \hat{i}+2 \hat{j}+3 \hat{k}) \times(3 \hat{i}-6 \hat{j}-2 \hat{k})}{|(6 \hat{i}+2 \hat{j}+3 \hat{k}) \times(3 \hat{i}-6 \hat{j}-2 \hat{k})|}=\frac{2 \hat{i}+3 \hat{j}-6 \hat{k}}{7}$

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