# Vectors – Calculate the length of diagonals of a parallelogram – Exercise 4469

Exercise

Calculate the lengths of the parallelogram diagonasl built on the vectors

$$\vec{a}=5\vec{p}+2\vec{q}$$

$$\vec{b}=\vec{p}-3\vec{q}$$

Given that

$$|\vec{p}|=2\sqrt{2}, |\vec{q}|=3$$

And the angle between them is equal to 45 degrees.

$$|\vec{a}+\vec{b}|=15$$
$$|\vec{b}-\vec{a}|=\sqrt{593}$$