The value of \( \lambda \) for which the vectors \( 3\hat{\imath}+6\hat{\jmath}-\hat{k} \) and \( -2\hat{\imath}+4\hat{\jmath}-\lambda\hat{k} \) are perpendicular is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → −18
Two vectors are perpendicular exactly when their dot product is zero:
\( \displaystyle (3)(-2)+(6)(4)+(-1)(-\lambda)=0 \)
\( \displaystyle -6+24+\lambda=0 \)
\( \displaystyle \lambda=-18 \)