Vectors Math Problem

Question

Let point C = (−2, 5), point D = (3, 8), and point E = (4, −1).

​Define u =  and v = .

a.​Sketch vectors u  and  v .

​b.​Sketch vector u + v  and compute it algebraically. Does this agree with your sketch?

Answer 1

Let point O(0, 0) represent origin which is a null vector at origin in coordinate plane.

Define vector u = OC + OD and vector v = OD + OE

Algebraically vector OC = -2i + 5j , vector OD = 3i + 8j and vector OE = 4i - 1j

here i and j are unit vectors in x & y directions respectively.

Therefore vector u = (-2+3)i + (5+8)j = 1i + 13j and vector v = (3+4)i + (8-1)j = 7i + 7j

Determine vector u + v by adding respective components i and j we get

Vector u + v = (1+7)i + (13+7)j = 8i + 20j

I plotted these vectors u, v and u + v on a graph paper. They match.