Question

If the scalar triple product of the vectors $-3\hat{i}+7\hat{j}-3\hat{k}$, $3\hat{i}-7\hat{j}+\lambda \hat{k}$ and $7\hat{i}-5\hat{j}-3\hat{k}$ is $272$ then $\lambda =......$

• A. $9$
• B. $11$
• C. $8$
• D. $10$

Answer 1

Answer: (B)

Scalar triple product of the given vectors is $272.$
$\therefore \left|\begin{array}{ccc}-3& 7& -3\\ 3& -7& \lambda \\ 7& -5& -3\end{array}\right|=272$ ($\because$ scalar triple product of the vectors a, b and $c$ is [a b c])
$\Rightarrow -3(21+5\lambda )-7(-9-7\lambda )-3(-15+49)=272$
$\Rightarrow -63-15\lambda +63+49\lambda -102=272$
$\Rightarrow 34\lambda -102=272$
$\Rightarrow 34\lambda =374$
$\Rightarrow \lambda =11$