Q136 / 180 · AIIMS 2013 · Physics

If a vector $2 \hat{i}+3 \hat{j}+8 \hat{k}$ is perpendicular to the vector $4 \hat{i}-4 \hat{j}+\alpha \hat{k}$, then value of $\alpha$ is

  • A
    $-1$
  • Correct answer
    B
    $\frac{1}{2}$
  • C
    $-\frac{1}{2}$
  • D
    $1$

Solution

For perpendicular vectors. $\vec{A} \cdot \vec{B}=0$ $\therefore \quad(2 \hat{i}+3 \hat{j}+8 \hat{k}) \cdot(4 \hat{i}-4 \hat{j}+\alpha \hat{k})=0$ $8-12+8 \alpha=0$ $-4+8 \alpha=0$ $\alpha=\frac{1}{2}$.

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

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