Question

Hi. Im looking for the formula to calculate the orthogonal projection of w onto the subspace spanned by u
and v. Where W,U,V are vectors

Answer 1

would that be the cross product of u and v?

Answer 2

or rather, if they exist all inthe same subspace and are orthogonal; then wouldnt the dot products betweenthem be zero?

Answer 3

orthogonal projection...... eh...

Answer 4

i dont know the formula, but it sounds intriguing ;)

Answer 5

here is a simple example that may help

Answer 6

lol..you said it was simple :)

Answer 7

The vectors themselves are as follows

u = 1 over the square root of 2 [-1]
[ 0]
[1]

v = 1 over the square root of 6 [1

Answer 8

v = 1 over the square root of 6 [1 ]
[-2]
[1]

w = [2]
[1]
[-3]

Answer 9

There is a formula for orthogonal projection but it is usually used between two vectors, you would have to figure out how to use it with a third. For example orthogonal projection of v on u is [(v dot u)/||u||^2]multiplied by vector u