Question

Let $x_0$ be the point of local minima of $f(x) = \vec{a} \cdot (\vec{b} \times \vec{c})$ where $\vec{a} = x\hat{i} - 2\hat{j} + 3\hat{k}$, $\vec{b} = -2\hat{i} + x\hat{j} - \hat{k}$, $\vec{c} = 7\hat{i} - 2\hat{j} + x\hat{k}$, then value of $\vec{a} \cdot \vec{b}$ at $x = x_0$ is

• A. 15
• B. -15
• C. 12
• D. -12

Hint:

To find local extrema for a function defined by a scalar triple product, first expand the determinant to get the function in polynomial form. Then apply standard calculus techniques (first and second derivative tests) to find the points of local minimum or maximum.

Answer 1

The Correct Option is A