Question

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

Answer 1

The lengths of the two diagonals of the parallelogram are 1 and √5.

Step-by-step explanation:

To find the lengths of the two diagonals of a parallelogram, we can use the properties of vectors. Given vectors u = ⟨-1,0⟩ and v = ⟨1,1⟩, the sum u + v represents one diagonal of the parallelogram, while the difference u - v represents the other diagonal.

To calculate the lengths of these diagonals, we can use the formula for the magnitude of a vector: √(x^2 + y^2). Plugging in the values for u + v and u - v, we get √((-1 + 1)^2 + (0 + 1)^2) = √(0^2 + 1^2) = √1 = 1 for the first diagonal, and √((-1 - 1)^2 + (0 - 1)^2) = √((-2)^2 + (-1)^2) = √(4 + 1) = √5 for the second diagonal.