The value of $m$ for which the volume of the parallelepiped is $4$ cubic units with edges $\vec a = m\hat i + \hat j + \hat k$, $\vec b = \hat i - \hat j + \hat k$, $\vec c = \hat i + 2\hat j - \hat k$ is
- A. $-1$
- B. $1$
- C. $0$
- D. $-2$
✅ Correct Answer: $1$
Explanation
Volume is given by $|\vec a \; \vec b \; \vec c|$ $= \begin{vmatrix} m & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 2 & -1 \end{vmatrix}$ $= -m + 5$ So $m = 1$
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