Question

Write the projections of \[\vec{r} = 3 \hat{i} - 4 \hat{j} + 12 \hat{k}\] on the coordinate axes. 

Answer 1

We have
\[ \vec{r} = 3 \hat{i} - 4 \hat{j} + 12 \hat{k} \]
\[\text{ Projection of } \vec{r} \text{ on x-axis }=\frac{\vec{r} . \hat{i}}{\left| \hat{i} \right|}=\frac{3}{1}=3\]
\[\text{ Projection of } \vec{r} \text{ on y-axis }=\frac{\vec{r} . \hat{j}}{\left| \hat{j} \right|}=\frac{- 4}{1}=-4\]
\[\text{ Projection of } \vec{r} \text{ on z-axis }=\frac{\vec{r} . \hat{k}}{\left| \hat{k} \right|}=\frac{12}{1}=12\]