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Visualization of my question

also kudos to your superb equation typing skills :)

As far as where the far RHS of the equation is derived from... Let me see what I can figure out.

cos θ = sqrt2/2 = sin θ ... but i'm still confused about the LHS!

The projection would be equal to a.\[r_x=a \hat i; r_y=a\hat j\]I believe.

yes! then r_13 = a(i^ + j^) ?
but the answer shows r_13 = sqrt2/2 (i^ + j^)
:E

the factor of r may have been lost due to the fact that it is a unit vector...
i'm not sure myself