Question

If the volume of the parallelopiped with coterminous edges 4$\overrightarrow{i}$ +5$\overrightarrow{j}$ + $\overrightarrow{k}$, -$\overrightarrow{j}$ + $\overrightarrow{k}$ and 3$\overrightarrow{i}$ + 9$\overrightarrow{j}$ +p$\overrightarrow{k}$ is 34 cubic units, then p is

• A. $4$
• B. $-13$
• C. $-7$
• D. $7$

Answer 1

The correct option is B $-13$

Volume of parallelopipe$=\left[\begin{array}{ccc}a& b& c\end{array}\right]$

$⟹Volume=\left|\begin{array}{ccc}4& 5& 1\\ 0& -1& 1\\ 3& 9& p\end{array}\right|=34$

$⟹4(-p-9)-5(-3)+1\left(3\right)=34$

$⟹-4p-36+15+3=34$

$⟹-4p-18=34$

$⟹-4p=52$

$⟹p=\frac{-52}{4}=-13$