# Thread: orthogonal projection

1. ## orthogonal projection

= (4, -1, 10) and = (-7, 0, 10) be vectors. Find the orthogonal projections of onto .

How would i go about this?

2. The vector component of $\bold{b}$ orthogonal to $\bold{a}$ is given by: $\bold{b} - \text{proj}_{\bold{a}} \bold{b} \ = \ \bold{b} - \frac{\bold{b} \cdot \bold{a}}{|\bold{a}|^2}\bold{a}$

Just a matter of calculations from there.