Keep the same vector w as in the diagram. Visualize projecting w onto various vectors v'. Can you think of a vector v' that results in a projection kv' that collapses both the y and z dimensions of w ?

A good answer might be:

It is probably harder to read the question than to figure out the result. If w = (4, 2.5, 2.5)^T is projected onto v' = (1, 0, 0)^T the result is kv = (4, 0, 0)^T

Another Example

Of course, that is what coordinate axes are: when a vector in 3D space is projected onto a coordinate axes you get one of the three dimensions of that vector. So let us look at an example that is not quite so easy:

In the picture w = (4, 2, 3)^T and v = (6, 4, 2)^T.

QUESTION 16:

Visually project w onto v.