Suppose u ¯ = ⟨ 3 , − 3 ⟩ and v ¯ = ⟨ 15 , − 3 ⟩ are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are?

Answer 1

The diagonals are u+v and u-v.

u+v = <3,-3> + <15,-3> = <18,-6> and its magnitude (length) is ||u+v|| = sqrt (18^2 + (-6)^2) = sqrt(360) = sqrt(36*10) = 6sqrt(10)

u-v = <3,-3> - <15,-3> = <-12,0> and its magnitude (length) is ||u-v|| = sqrt((-12)^2 + 0^2) = sqrt(144) = 12