Q102 / 150 · MHT CET 2026 (20 April Shift 2) · Physics

If two vectors $\vec{A} = 4\hat{i} + n\hat{j} + 2\hat{k}$ and $\vec{B} = 2\hat{i} + 2\hat{j} - \hat{k}$ are mutually perpendicular to each other then value of 'n' is

  • A
    $+3$
  • B
    $+1$
  • Correct answer
    C
    $-3$
  • D
    $-1$

Solution

For two vectors to be mutually perpendicular, their dot product must be zero.

$\vec{A} \cdot \vec{B} = 0$

$(4\hat{i} + n\hat{j} + 2\hat{k}) \cdot (2\hat{i} + 2\hat{j} - \hat{k}) = 0$

$(4)(2) + (n)(2) + (2)(-1) = 0$

$8 + 2n - 2 = 0$

$2n + 6 = 0$

$n = -3$

Answer: $-3$

Hence, the correct answer is option: 'C'.

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