find the distances of OA,OB and AB of (3,3√3) and (2√3,0)

Answer 1

To find the distances of OA, OB, and AB for the two given points, we first need to calculate the coordinates of point A and point B.

Point A: (3, 3√3)
Point B: (2√3, 0)

Now, we can find the distances:

OA = √((3-0)^2 + (3√3-0)^2)
= √(9 + 27)
= √36
= 6

OB = √((2√3-0)^2 + (0-0)^2)
= 2√3

AB = √((3-2√3)^2 + (3√3-0)^2)
= √(9 - 12√3 + 12 + 27)
= √(36 + 27 - 12√3)
= √63 - 6√3

Therefore, the distances are:
OA = 6
OB = 2√3
AB = √63 - 6√3