# vector

• Dec 9th 2008, 12:47 PM
fastcarslaugh
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
• Dec 10th 2008, 02:49 PM
o_O
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.
• Dec 10th 2008, 02:53 PM
fastcarslaugh
No..

that gives me vector projection.
• Dec 10th 2008, 03:32 PM
fastcarslaugh
$\displaystyle \frac {36}{42}v_1 + \frac {27}{98}v_2 + \frac{45}{98}v_3 = 0$

How would I find these three points.
Because $\displaystyle {u}\cdot{v} = 0$ means that they are perpendicular to each other