Question

Use the vectors u u un un), v (v, v n), and w (wi wa wn) to verify the following algebraic properties of R a) (u v) w u (v w) b) c(u v) cu cv for every scalar c

Answer 1

a) To verify (u v) w = u (v w), we can use the distributive property of the dot product:

(u v) w = (u ∙ v) w = (v ∙ u) w = v (u ∙ w) = v (w ∙ u) = u (v ∙ w)

Therefore, (u v) w = u (v w).

b) To verify c(u v) = cu cv, we can use the distributive property of scalar multiplication:

c(u v) = c(u ∙ v) = (cu) v = (cv) u = cu cv

Therefore, c(u v) = cu cv.