Use vectors to demonstrate that on a circle any two diametrically opposed points along with an arbitrary third point(on the circle) form a right triangle
Hint: assume without a loss of generality that the circle is centered at the origin and let v, -v, and w denote the three points in question. show that the vector connecting w to -v is orthogonal to the vector connecting w to v
The Attempt at a Solution
i think i have a grasp on how to achieve this. to show that they are orthogonal the dot product of the two vectors must be 0.
I am confused with the v and -v. In my mind that makes a straight line for example say that v is (1,0) then -v would be (-1,0).
I dont see how those two points along with a third make a right triangle.