Orthogonal projection onto a plane spanned by two vectors

[shreddinglicks]

Homework Statement

x = <0, 10, 0>
v1 = <4, 3, 0>
v2 = <0, 0, 1>

Project x onto plane spanned by v1 and v2

Homework Equations

Projection equation

The Attempt at a Solution

I took the cross product
k = v1xv2 = <3, -4, 0>

I projected x onto v1xv2
[(x*k)/(k*k)]*k = <-4.8, 6.4, 0 = p

I finished by
x - p = <4.8,3.6,0>

Is this correct?

 

[andrewkirk]

You can check this as follows:

Step 1: check that (x-p) is in the plane, ie check that it can be expressed as a linear combination of v1 and v2.
Step 2: check that (x-p) is perpendicular to p (take the dot product)
Step 3: check that (x-p) + p = p

If these are all correct then the solution is correct.