For three vectors A = (-xi - 6j - 2k), B = (-i + 4j + 3k) and C = (-8i - j + 3k), if A · (B × C) = 0, then value of x is ________. Numerical answer type. Work it out, then open the answer.

Answer: 4. B × C = i[(4)(3) - (3)(-1)] - j[(-1)(3) - (3)(-8)] + k[(-1)(-1) - (4)(-8)] = 15i - 21j + 33k A · (B × C) = -15x + 126 - 66 = 60 - 15x = 0 So x = 4.

For three vectors A = (-xi - 6j - 2k), B = (-i + 4j + 3k) and C =… | JEE Main 2024 (6 Apr, Shift 1)

Q7JEE Main 2024 · 6 APR · SHIFT 1Medium

Vector (Cross) Product

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 value of $x$ is ________.

Numerical answer type. Work it out, then open the answer.

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Answer: 4

$\vec{B} \times \vec{C} = \hat{i}[(4)(3) - (3)(-1)] - \hat{j}[(-1)(3) - (3)(-8)] + \hat{k}[(-1)(-1) - (4)(-8)]$
$= 15\hat{i} - 21\hat{j} + 33\hat{k}$
$\vec{A} \cdot (\vec{B} \times \vec{C}) = -15x + 126 - 66 = 60 - 15x = 0$
So $x = 4$ .

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Vector (Cross) Product question from JEE Main 2024 (6 Apr, Shift 1)

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