# Find vectors that produce certain orthogonal projection

1. Sep 12, 2011

### fmilano

I have vector [ tex ] v [ /tex ] produced by an orthogonal projection of vector [ tex ] w [ /tex ] over plane spanned by vectors [ tex ] u_1 [ /tex ] and [ tex ] u_2 [ /tex ], in a three dimensional space. If I know [ tex ] v [ /tex ], [ tex ] u_1 [ /tex ] and [ tex ] u_2 [ /tex ], how could I calculate [ tex ] w [ /tex ]?

Thanks in advance,

Federico

2. Sep 12, 2011

### micromass

So you want to calculate the orthogonal projection on the space spanned by u1 and u2.

There is a formula for that:

$$w=\frac{<v,u_1>}{<u_1,u_1>}u_1+\frac{<v,u_2>}{<u_2,u_2>}u_2$$

To write in LaTeX, you don't need to write the space in [ tex ] and [ /itex ]

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