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Motion in A Plane question

2005 · Q158
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Motion in A Plane question

2005 · Q158

NEETPhysicsMotion in A PlaneMCQ+4 / −1
If a vector 2i^+3j^+8k^2\widehat i + 3\widehat j + 8\widehat k2i+3j​+8k is perpendicular to the vector 4j^−4i^+αk^,4\widehat j - 4\widehat i + \alpha \widehat k,4j​−4i+αk, then the value of α\alphaα is
  1. A
    1/2
  2. B
    −-− 1/2
  3. C
    1
  4. D
    −-− 1.
View written solutionFree

Correct answer: B

For two vectors to be perpendicular to each other
A→.B→=0{\overrightarrow A .\overrightarrow B = 0}A.B=0

(2i^+3j^+8k^).(4j^−4i^+αk^)=0\left( {2\widehat i + 3\widehat j + 8\widehat k} \right).\left( {4\widehat j - 4\widehat i + \alpha \widehat k} \right) = 0(2i+3j​+8k).(4j​−4i+αk)=0

–8 + 12 + 8α\alpha α = 0

α=−48=−12\alpha = - {4 \over 8} = - {1 \over 2}α=−84​=−21​

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