A parallelogram is defined by vectors OA=(4,3) and OB=(1,1). Determine the length of the diagonals
OA+OB=(4,3)+(1,1)
=(5,4)
sqrt(5^2+4^2)
=6.403
OA-OB=(3,2)
sqrt(3^2+2^2)=3.60
Therefore the length of diagonals are 6.40 and 3.60 units.
To determine the length of the diagonals of a parallelogram defined by vectors OA and OB, you need to find the magnitude of the sum and the difference of these vectors.
1. Start by finding the sum of vectors OA and OB:
OA + OB = (4,3) + (1,1) = (4+1, 3+1) = (5,4)
2. Find the magnitude of the sum:
||OA + OB|| = sqrt(5^2 + 4^2) = sqrt(25 + 16) = sqrt(41) ≈ 6.403
So, the length of one diagonal is approximately 6.403 units.
3. Next, find the difference of vectors OA and OB:
OA - OB = (4,3) - (1,1) = (4-1, 3-1) = (3,2)
4. Find the magnitude of the difference:
||OA - OB|| = sqrt(3^2 + 2^2) = sqrt(9 + 4) = sqrt(13) ≈ 3.606
Thus, the length of the other diagonal is approximately 3.606 units.
Therefore, the length of the diagonals of the parallelogram is approximately 6.403 units and 3.606 units.