MHB Projection of $\overrightarrow{c}$ on $\overrightarrow{a}$: Example

[mathmari]

Hey!

To find the projection of $\overrightarrow{c}$ on $\overrightarrow{a}$ do we have to use the formula $$\frac{\overrightarrow{c} \cdot \overrightarrow{a}}{||\overrightarrow{a}||^2}\overrightarrow{a}$$ ?? (Wondering)

For example, if we have $\overrightarrow{c} =(4, 2, -6)$ and $\overrightarrow{a}=(-2, 2, 2)$ :

$$\frac{(4, 2, -6) \cdot (-2, 2, 2)}{||(-2, 2, 2)||^2}(-2, 2, 2)=\frac{-8+4-12}{4+4+4}(-2, 2, 2)=\frac{-16}{12}(-2, 2, 2)=\frac{-4}{3}(-2, 2, 2)$$

Is this the asked projection?? (Wondering)

 

[Dethrone]

Yes, that is correct, assuming you are to compute the vector projection. (Yes)

 

[mathmari]

Yes, that is correct, assuming you are to compute the vector projection. (Yes)

Great! Thank you! (Yes)