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Consider the vectors v,w,x and y in the picture below:

We will project each of these vectors onto $$\mathbf{u} = \begin{pmatrix} 1\\ 1 \end{pmatrix}$$, pictured below:

The projections are the list a,b,c,d in some order:

What order do we put a,b,c,d in such that the first vector is the projection of v onto u, the second vector is the projection of w onto u, the third vector is the projection of x onto u, and the fourth vector is the projection of y onto u?

Sep 18, 2020

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v and u are at right angles, so v projected onto u is a zero length vector (i.e. the dot).

.w is in the opposite direction to u so the projection will be facing the opposite way from u (i.e. a)

x is a small amount in the same direction as u so its projection will be small and in the same direction as u (i.e. c)

I'll leave you to reason about te projection of y onto u.

Sep 18, 2020
edited by Alan  Sep 18, 2020