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

One diagonal is the vector u + v= < 1, 0 > + <2, -3>= < 3, - 3 > and its

length is || u + v || = √( 3 )² + ( -3 )²=√ 9+9 =√18 =3√2.

The other diagonal is the vector u − v= < 1, 0 > − <2, -3>= < -1, 3 > and its

length is || u − v || = √( -1 )² + ( 3 )²=√ 1+9 =√10 .