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