Compute the following, then sketch each resultant vector.

Question

u = <7,3>, v = <-4,0>

(a) u+v = _____

top left: a, top right: b, bottom left: c, bottom right: d

(b) u-v = ______

top left: a, top right: b, bottom left: c, bottom right: d

(c) 2u - 3v = _____

top left: a, top right: b, bottom left: c, bottom right: d

(d) 1/2v + 4u = _____

top left: a, top right: b, bottom left: c, bottom right: d

Answer 1

You can use the definitions of vector addition, difference and Scalar multiplication.

Let u =< u_{1 ,}u₂ > and v = <v₁, v₂>. Then

u + v = <u₁ + u₂ >

u – v = u + (– v) = <( u₁ – v₁ ) , (u₂ – v₂ ) >

The scalar multiple of c and u is the vector cu = < cu₁ , cu₂ >

Please follow the definitions and compute accordingly.