Question

The value of 'a' for which the scaler triple product formed by the vectors $\vec\alpha=\hat{i}+a\hat{j}+\hat{k}$, $\vec{\beta}=\hat{j}+a\hat{k}$ and $\vec{\gamma}=a\hat{i}+\hat{k}$ is maximum, is

• A. 3
• B. -3
• C. $\frac{1}{\sqrt3}$
• D. $-\frac{1}{\sqrt3}$

Answer 1

Answer: (D)

$-\frac{1}{\sqrt3}$

Answer 2

$\begin{vmatrix} 1 &a &1 \\\ 0&1 &a \\\ a& 0 &1 \end{vmatrix}$
$=1-a(-a^2)-a$
$=1+a^3-a$
differentiating we get, $\frac{\alpha v}{qa}=3a^2-1=0$
$q\equiv \frac{-1}{\sqrt3}$
So, the correct option is (D) : $\frac{-1}{\sqrt3}$