Question

n = 2i + j - k is a normal vector to the plane 2x + y - z = 1. Decompose the vector k (a unit vector pointing from the point (0, 0, -1) to (0, 0, 0)) into the sum of two vectors; one of them is parallel to n and the other one is orthogonal to n.

Answer 1

find where the line with the given direction vector thru the given point, pierce thru the plane, and also the point where a line with the normal vector as a direction vector, thru the origin pierces thru the plane .... this creates 2 points that forms the other leg of a right triangle that defines the perp vector. then just scale the results

Answer 2

i spose the vector k is meant to be represented as a position vector and therefore can be generated thru the origin as well ....