If a vector 2i^ + 3j^ + 8k^ is perpendicular to the vector 4i^ -4j^+ αk^, then value of α is :

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

A
-1
B
$- \frac{1}{2}$
C
1/2
D
1

Solution:

$(2 \hat{i} + 3 \hat{j} + 8 \hat{k}) . (4 \hat{i} - 4 \hat{j} + α \hat{k}) = 0 \Rightarrow 8 - 12 + 8 α = 0 \Rightarrow α = \frac{1}{2}$

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