Find the orthogonal projection of the point M(1,2,8) in the line \frac{x+1}{2}=\frac{y-2}{-1}=\frac{z}{1}.

How will I find the orthogonal projection?

Did you check under the couch?

I solved it like system of:

\frac{x+1}{2}=\frac{y-2}{-1}=\frac{z}{1}

2\sqrt{11}=\sqrt{(x-1)^2+(y-2)^2+(z-8)^2}

Is this correct?

Write the line equation in the form P+nt where P is a point, n is a vector (along the line, of course) and t is a parameter. Let the orthogonal projection of M be K. Then it should be (M-P).n=t(n.n) where K=P+nt.