The value of \(\lambda\) for which the vectors \(2\hat{\imath}+\lambda\hat{\jmath}+\hat{k}\) and \(\hat{\imath}-2\hat{\jmath}+3\hat{k}\) are perpendicular is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{5}{2}\)
Two non-zero vectors are perpendicular exactly when their scalar product is zero.
\((2\hat{\imath}+\lambda\hat{\jmath}+\hat{k})\cdot(\hat{\imath}-2\hat{\jmath}+3\hat{k}) = 0\)
\(2(1)+\lambda(-2)+1(3) = 0\)
\(5-2\lambda = 0\)
\( \displaystyle \lambda = \frac{5}{2} \)