Suppose u 2 0 and v 4 2 are two vectors that form the side

Suppose u- = 2, 0 and v- = 4, -2 are two vectors that form the sides of a parallelogram, Then the lengths of the two diagonals of the parallelogram are

Solution

One diagonal is sum of both vectors = < 6, -2 >

length of diagonal = sqrt(6^2 + 2^2) = sqrt(40) = 2sqrt10

Other diagonal is difference between two vectors = < -2 , 2 >

length of other diagonal = sqrt(2^2 + 2^2) = sqrt8 = 2sqrt2