Question

Compute the lengths of the diagonals of the parallelogram determined by $u=i$ and $v=2j$.

Short answer

The lengths of diagonals are $\sqrt{5}$ and $\sqrt{5}$.

Step-by-step solution

Given Information

The sides of a parallelogram are $u=i$ and $v=2j$.

The lengths of the diagonal of a parallelogram $u+v$ and $u-v$.

Find the diagonal vector of the parallelogram

First diagonal $(u+v)=i+2j$.

Second diagonal $(u-v)=i-2j$.

Find the length of the diagonals

The length of the first diagonal:

$=\sqrt{1^2+2^2}$

$=\sqrt{5}$.

The length of the second diagonal:

$=\sqrt{1^2+(-2{)}^2}$

$=\sqrt{5}$.