Q 11-03-065JEE MainJEE Main 2024 (6 Apr, Shift 1)Medium
For three vectors $\vec A = (-x\hat i - 6\hat j - 2\hat k)$, $\vec B = (-\hat i + 4\hat j + 3\hat k)$ and $\vec C = (-8\hat i - \hat j + 3\hat k)$, if $\vec A\cdot(\vec B\times\vec C) = 0$, then the value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 4
$$\vec A\cdot(\vec B\times\vec C) = \begin{vmatrix} -x & -6 & -2 \\ -1 & 4 & 3 \\ -8 & -1 & 3 \end{vmatrix} = -x(12 + 3) + 6(-3 + 24) - 2(1 + 32)$$
$$= -15x + 126 - 66 = -15x + 60 = 0 \Rightarrow x = 4$$
Solution by Sreeraj P, M.Sc Physics