Question

Write the projection of $\hat{i}+\hat{j}+\hat{k}$ along the vector $\hat{j}$.

Answer 1

$$\begin{gathered} \text{Projection of}\overrightarrow{a}\text{on}\overrightarrow{b}\text{=}\frac{\overrightarrow{a}.\overrightarrow{b}}{\left|\overrightarrow{b}\right|} \\ \text{Projection of}\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}\text{along}\overrightarrow{j} \\ =\frac{\left(\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}\right).\overrightarrow{j}}{\left|\overrightarrow{j}\right|} \\ =\frac{1}{1} \\ =1 \end{gathered}$$