A parallelogram is formed by the vectors = (2, 3) and = (1,

1).

a) Determine the lengths of the diagonals.

b) Determine the perimeter of the parallelogram.

a) 5 and √5

b) P = 2 * √13 + 2 * √2

Step-by-step explanation:

We add the two vector and for definition the result will be one of the diagonal of the parallelogram. Then

vector OA (2, 3) vector OB (1. 1)

If vector OD = OA + OB then

coordinates of OD will be (2 + 1, 3 + 1) (3, 4)

And the length of OD is according to Pythagoras Theorem

|OD| = √ (3) ² + (4) ² = √ 9 + 16 = √25 = 5

For the other diagonal we need to apply the subtraction of vectors wich will give us the other diagonal

vector OA = (2, 3) and vector OB = (1, 1)

If vector BA is the difference between vectors OA - OB then vector BA is

vector BA = (2 - 1, 3 - 1) = (1, 2)

And the length of BA is according to Pythagoras Theorem

BA = √ (1) ² + (2) ² = √1 + 4 = √5

Then the length of the other diagonal is √ 5

b) To find the perimeter of the parallelogram we need to apply

Perimeter = 2 OA + 2 OB

P = 2 OA + 2 OB (1)

So length of OA is:

|OA| = √ (2) ² + (3) ² = √ 13

and

|OB| = √ (1) ² + (1) ² = √2

Then by subtitution in (1)

P = 2 * √13 + 2 * √2