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If a vector 2î + 3ĵ + k̂ is perpendicular to the vector 4ĵ − 4î + αk̂, then the value of α is

1. 1/2
2. −1/2
3. 1
4. −1

Correct answer: 1/2

Solution

Two vectors are perpendicular if their dot product is zero. The dot product of (2î + 3ĵ + k̂) and (−4î + 4ĵ + αk̂) is -8 + 12 + α = 0. Solving for α gives α = 1/2.

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