This question came in the admission exam of Rajshahi University in 2020-21
Q) If two vectors $2\hat{i}+3\hat{j}+\hat{k}$ and $-4\hat{i}-6\hat{j}-\lambda\hat{k}$ are mutually perpendicular, then what will be the value of $\lambda$?
(A) 2
(B) -2
(C) 0.5
(D) -0.5
None of the options seem correct. The correct value of $\lambda$ will be -26 if the two vectors are perpendicular. Do they mean parallel? If the two vectors are parallel, then the value of $\lambda$ will be (A).
Best Answer
If the two vectors are perpendicular, then:
\begin{equation*} -8-18-\lambda =(2,3,1) \cdot (-4,-6,-\lambda) = 0 \end{equation*}
Therefore, $\lambda = -26$.
If the two vectors are parallel, then:
\begin{equation*} (-3\lambda+6,2\lambda -4,0) =(2,3,1) \times (-4,-6,-\lambda) = (0,0,0) \end{equation*}
Therefore, $\lambda = 2$. What you claim is most likely correct.