Projecting a vector onto a plane

[fishingspree2]

Homework Statement

Project a vector into the plane x + 3y + 2z = 0 in the direction d = 2i + j - k

The Attempt at a Solution

Let u = ai + bj +ck, a vector in R^3.
then u + t*d = (a+2t)i + (b+t)j + (c-t)k where t is a real number

when u + t*d hits the plane then

(a+2t) + 3(b+t) + 2(c-t) = 0
solve for t, substitute into u = t*d, then plug in the a,b,c values for the vector to be projected

Is this approach correct?

Thank you very much

 

[HallsofIvy]

I presume that you mean "project the vector 2\vec{i}+ \vec{j}+ \vec{k}[/tex] onto the plane x+ 3y+ 2z= 0. <br /> <br /> Use the fact that the vector \vec{i}+ 3\vec{j}+ 2\vec{z}[/tex] is perpendicular to the plane. Project the given vector onto that normal vector, then subtract that from the given vector.

 

[fishingspree2]

Hello,

No i meant project some vector on the plane in a direction parallel to 2i + j + k, which is not an orthogonal projection.