If a vector 2i^+3j^+8k^ is perpendicular to the vector 4j^−4i^+αk^. Then the value of α is

Given vectors can be rewritten as $\vec{A} = 2 \hat{i} + 3 \hat{j} + 8 \hat{k}$ and $\vec{B} = - 4 \hat{i} + 4 \hat{j} + α \hat{k}$

Dot product of these vectors should be equal to zero because they are perpendicular.

$\begin{array}{l} ∴ \vec{A} \cdot \vec{B} = - 8 + 12 + 8 α = 0 \\ \Rightarrow 8 α = - 4 \\ \Rightarrow α = - 1 / 2 \end{array}$

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