10. Let the projection point P(a, b, c), then MP intersects the known straight line vertically.

If p is on a straight line, (a+1)/2 = (b+2)/1= (c-1)/(-1) = t.

a = 2t- 1，b = t-2，c = -t+ 1

The direction vector of MP is (a- 1, b- 1, c- 1).

Then 2 (a-1)+1(b-1)-1(c-1) = 0, which means 2a+b-c = 2.

4t-2 + t-2 + t- 1 = 2，6t = 7，t = 7/6，

P(4/3，-5/6，- 1/6)