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AIIMS 2013
Exam
AIIMS
Year
2013
Subject
Physics
Chapter
Mathematics in Physics

AIIMS 2013 · Physics · Mathematics in Physics

If a vector 2 i +3 j +8 k is perpendicular to the vector 4 i -4 j...

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

Options

  1. A−1-1
  2. B12\frac{1}{2}
  3. C−12-\frac{1}{2}
  4. D11

Correct answer

B. 12\frac{1}{2}

Step-by-step solution

For perpendicular vectors. A⃗⋅B⃗=0\vec{A} \cdot \vec{B}=0 ∴(2i^+3j^+8k^)⋅(4i^−4j^+αk^)=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+8α=08-12+8 \alpha=0 −4+8α=0-4+8 \alpha=0 α=12\alpha=\frac{1}{2}.
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