2
$\begingroup$

An isosceles triangle is formed by a unit vector in the x-direction and another in a random direction. Find the distribution of the length of the third side in three dimensions.

I know how to do this problem in two dimensions. The angle varies with uniform distribution, so after some trigonometry and calculation, you get (2/pi)arcsin(x/2). In three dimensions, the angle that varies is the angle between the random vector and the x-y plane. Then I'm stuck as to how the angle relates to the length of the third side (if at all).

Thanks so much!

  • 1
    Is the vector in the random direction a unit vector? If so, your distribution will depend on two angles...2011-04-26

1 Answers 1