Question

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 \( \vec{A} \cdot(\vec{B} \times \vec{C})=0 \), them value of \( x \) is \( \qquad \) - [NCERT : PL-102, 103|April 6, 2024 (I)]

Answer 1

A.(BXC) = 0 =   det |-x   -6  -2   |
                               | -1   4    3  |
                               | -8   -1   3  |

expanding using first column

0 = -x ( 12 + 3)  + ( -18 - 2) - 8 ( -18 + 8)

0 = -15x -20  + 80

15x = 60

x = 4