given v=5i+3j and w=-4i+8j, find projwv

Answer 1

There are two kinds of projection of w on to v or of v on to w.
You did not say projection of which on the other or if you want scalar or vector projection.
see below:
Projections

One important use of dot products is in projections. The scalar projection of b onto a is the length of the segment AB shown in the figure below. The vector projection of b onto a is the vector with this length that begins at the point A points in the same direction (or opposite direction if the scalar projection is negative) as a.

Thus, mathematically, the scalar projection of b onto a is |b|cos(theta) (where theta is the angle between a and b) which from (*) is given by

This quantity is also called the component of b in the a direction (hence the notation comp). And, the vector projection is merely the unit vector a/|a| times the scalar projection of b onto a:

Thus, the scalar projection of b onto a is the magnitude of the vector projection of b onto a.

Answer 2

Here:
http://www.math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/dotprod/dotprod.html

Answer 3

it was proj with w as a subscript of proj and then v

Answer 4

I am sorry. I am not familiar with that notation. Follow the recipe in the link I gave you.