
vector
Let a = (8, 3, 5) and b = (8, 10, 5) be vectors. Find the scalar, vector, and orthogonal projections of b onto a .
I was able to easily find the scalar and vector projection, but I need help on orthogonal projection. All I know is that the dot production must equal 0.
Scalar projection = $\displaystyle 9/sqrt(98)$
Vector projection = ( $\displaystyle 36/49$ , $\displaystyle 27/98$ , $\displaystyle 45/98$ )
Thanks

The orthogonal projection of b onto a is given by: $\displaystyle \text{proj}_{\bold{a}} \bold{b} = \frac{\bold{b} \cdot \bold{a}}{ \bold{a} ^2} \bold{a}$
Just plug n' chug.

No..
that gives me vector projection.

$\displaystyle \frac {36}{42}v_1 + \frac {27}{98}v_2 + \frac{45}{98}v_3 = 0$
How would I find these three points.
Because $\displaystyle {u}\cdot{v} = 0$ means that they are perpendicular to each other