Vectors 3 Question 16
16. The volume of the parallelopiped whose sides are given by $\overrightarrow{\mathbf{O A}}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}, \overrightarrow{\mathbf{O B}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$,
$\overrightarrow{\mathbf{O C}}=3 \hat{\mathbf{i}}-\hat{\mathbf{k}}$, is
(1983, 1M)
(a) $\frac{4}{13}$
(b) 4
(c) $\frac{2}{7}$
(d) None of these
Show Answer
Answer:
Correct Answer: 16. (b)
Solution:
- The volume of parallelopiped $=[\overrightarrow{\mathbf{a}} \overrightarrow{\mathbf{b}} \overrightarrow{\mathbf{c}}]=\left|\begin{array}{ccc}2 & -3 & 0 \ 1 & 1 & -1 \ 3 & 0 & -1\end{array}\right|$
$$ =2(-1)+3(-1+3)=-2+6=4 $$
