Find u + v, u − v, and 2u − 5v. Then sketch each resultant vector.

Question

u = 5i, v = j

(a) u + v =

(b) u − v =

(c) 2u − 5v =

Answer 1

First of all: i = <1, 0> and j = <0, 1>

u = 5i =5*<1, 0> = <5, 0>

v = j = <0, 1>

u+v = <5, 0> + <0, 1> = <5, 1>

You graph <5, 1> the same way you would graph the point (5,1). Then draw an arrow from the origin to the point (5, 1) to create the vector! It should be the diagonal of the parallelogram (in this case rectangle) created from u and v, where u is the ray from the origin to the point (5, 0) and v is the ray from the origin to the point (0, 1).

Hope this helps you complete the others!