Let u (u 1 , u 2 , u 3 ), v (v 1 , v 2 , v 3 ), and w (w 1 , w 2 , w 3 ) Let c be a scalar Prove the following vector properties a Show that (u v) (u v) u 2u v v b Show that (u v) (u v) u v if u is perpendicular to v c Show that (u v) (u v) u v

Question: Let u = (u 1 , u 2 , u 3 ), v = (v 1 , v 2 , v 3 ), and w

Let u = (u₁, u₂, u₃), v = (v₁, v₂, v₃), and w = (w₁, w₂, w₃). Let c be a scalar. Prove the following vector properties.

$. a. Show that (u + v) (u + v) = \u$

. a. Show that (u + v) (u + v) = \u + 2u.v + |v|. b. Show that (u + v) (u + v) = ]u[ + |v| if u is perpendicular to v. c. Show that (u + v) (u v) = ]u[ |v|. -

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