Answer:
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
