Consider the following u 4 18 v 3 4 Calculate projv u proj

Consider the following. u = (4, 18), v = (-3, 4) Calculate proj_v u. proj_v u = Resolve u into u_1 and u_2, where u_1 is parallel to v and u_2 is orthogonal to v. u_1 = u_2 =

Solution

u = 4i + 18j

v = -3i + 4j

a) u.v = -12 + 72 = 60

IuI = sqrt(340)

IvI = 5

Proj_vu = (u.v)*v/IvI^2 = (60/25)*(-3i + 4j) = (12/5)*(-3i + 4j)

b) u1 = Proj_vu = (12/5)*(-3i + 4j)

u2 = (4, 18) - (12/5)*(-3, 4)