A) 4
B) -13
C) 13
D) 6
Correct Answer: B
Solution :
Since, coterminus edges of a parallelepiped are \[4\hat{i}+5\hat{i}+\hat{k},-\hat{j}+\hat{k}\]and\[3\hat{i}+9\hat{j}+p\hat{k}\]and Volume of parallelepiped = 34 \[\therefore \] \[\left| \begin{matrix} 4 & 5 & 1 \\ 0 & -1 & 1 \\ 3 & 9 & p \\ \end{matrix} \right|=34\] \[\Rightarrow \]\[4\left| \begin{matrix} -1 & 1 \\ 9 & p \\ \end{matrix} \right|-5\left| \begin{matrix} 0 & 1 \\ 3 & p \\ \end{matrix} \right|+1\left| \begin{matrix} 0 & -1 \\ 3 & 9 \\ \end{matrix} \right|=34\] \[\Rightarrow \]\[4(-p-9)-5(-3)+1(3)=34\] \[\Rightarrow \]\[-4p-36+15+3=34\] \[\Rightarrow \]\[4p=-36+18-34\] \[\Rightarrow \]\[p=-\frac{52}{4}=-13\]You need to login to perform this action.
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