Let,
\(\vec{a} =( \vec{8i} + \vec{j})\)
\(\vec{b} = (\vec{i} + \vec{2j} - \vec{2k})\)
\(\vec{b}\) = \(\sqrt{1^2 + 2^2+ 2^2}\) = \(\sqrt{1+ 4+ 4}\) = \(\sqrt {9}\) = 3
\(\vec{b}\) = \(\frac{\vec{b}}{\vec{|b|}}\) = \(\frac{\vec{i}+\vec{2j}-\vec{2k}}{3}\)
∴ The projection of \((\vec{8i}+\vec{j})\) on \((\vec{i}+{2j}-\vec{2k})\) is \((\vec{8i}+\vec{j})\) \(\frac{\vec{i}+\vec{2j}-\vec{2k}}{3}\)
= \(\frac{8+2+0}{3}\) = \(\frac{10}{3}\)
