I have to solve this...

[|m|]

I have this problem math....

Find the orthogonal projection of point T(21,35,-22) on a plane that is defined with A(2,−1, 4),B(0,−3,−2) and C(−1, 1, 4).

I don't have any idea how to solve this and I need to send result up to 29th April.
I hope that someone could solve this.

P.S: Excuse me for my bad english.

 

[pka]

What is the definition of orthogonal projection of a point onto a plane?

 

[|m|]

I think I can't explain that in english... U have to find a point in this triangle plane (A, B, C). If you draw a line trough point T and this point the line would be right-angled to the plane.
Sorry, I don't know all math terms in english. I hope you'll understand.

 

[pka]

A very clear answer, thank you.
Do you know how to write the equation of the plane determined by points A, B, & C?
If \(\displaystyle R = \left\langle {x,y,z} \right\rangle ,\;N = \vec {AB} \times \vec {AC}\) then the plane is \(\displaystyle N \cdot \vec {AR} = 0\)

The line through T perpendicular to the plane is \(\displaystyle T + tN\).

Write the plane in rectangular coordinates. Write the line in parametric form.
Make the substitutions of the components of the line into the equation of the plane.
Solving for the parameter, you should find the point to be (-3,-1,-2).

 

[|m|]

pka, U save me. THANK YOU!