What is the projection of (2,5) onto (1,3) ?

First, you have to calculate the dot product of a (2, 5) and b (1, 3)

a · b = (2, 5) · (1, 3) = 2*1 + 5*3 = 17

Then, you have to calculate the magnitude of b

|b| = √ (1² + 3²) = √10

The scalar projection will be:

sp = (a · b) / |b| = 17/√10 = (17√10) / 10

The vector projection will be:

vp = [ (a · b) / |b|² ] b = 17/10 (1, 3) = (17/10, 51/10)