Suppose 𝑢⎯⎯⎯=⟨1,0⟩ u ¯ = ⟨ 1 , 0 ⟩ and 𝑣⎯⎯⎯=⟨2,−3⟩ v ¯ = ⟨ 2 , − 3 ⟩ are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are

Question

Suppose 𝑢⎯⎯⎯=⟨1,0⟩ u ¯ = ⟨ 1 , 0 ⟩ and 𝑣⎯⎯⎯=⟨2,−3⟩ v ¯ = ⟨ 2 , − 3 ⟩ are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are ????

Answer 1

u = <1, 0>; v = <2, - 3>.

d₁ + u + v = <3, -3>

IId₁II = √9 + 9 = 3√2;

d₂ = u - v = <- 1, 3>

IId₂II = √1 + 9 = √10