Published by:
CGP EDU Academic Team
Published on: September 11, 2026
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 the value of \(\alpha\) is
Text Solution
Verified by ExpertsThe correct answer is:
C
Given vectors can be rewritten as \vec{A} = 2\hat{i} + 3\hat{j} + 8\hat{k} and \(\vec{B} = -4\hat{i} + 4\hat{j} + \alpha \hat{k}\)
Dot product of these vectors should be equal to zero because they are perpendicular.
\ \ \(\vec{A} \cdot \vec{B} = -8 + 12 - 8 \alpha = 0\) ⇒ ⇒ \(8\alpha = -4\) ⇒ ⇒ \(\alpha = -\frac{1}{2}\)
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