let vector U = (vector u1, vector u2) vector V = (vector v1, vector v2) and vector W = (vector w1, vector w2) Prove each property using Cartesian vectors:

Question

a) (vector U+V)+W = vector U+(v+W)
b) k(vector U+V) = k vector U + k vector V
c) (k+m)vector U = k vector U + m vector U

Answer 1

U+V + W = (u1+v1, u2+v2)+(w1,w2)
= (u1+v1+w1 , u2+v2+w2)
=(u1,u2) + (v1+w1`, v2+w2)
= U + (V+W)

Do the others the same way.