If a vector $2\widehat{i}+3\widehat{j}+8\widehat{k}$ is perpendicular to the vector $4\widehat{i}-4\widehat{j}+\alpha \widehat{k}$ then the value of $\alpha$ is

For two vectors to be perpendicular to each other  $\overrightarrow{A}\cdot \overrightarrow{B}=0$
$(2\widehat{i}+3\widehat{j}+8\widehat{k})\cdot \left(\mathrm{4}i\mathrm{-}\mathrm{4}j\mathrm{+}\alpha k\right)=0\Rightarrow 8-12+8\alpha =0\text{ or }\alpha =\frac{4}{8}=\frac{1}{2}$