coordinates of 3rd point (vertex) of a right triangle knowing lengths and direction

Question

In a last post I wanted to know the 3rd point of vertex, actually I have some similar problem ....

I think I have all data.. for example...:

1. 3 vertex cordinates in order to have the direction(gray arrow):

    v1 = (-0.117, 1.06,0.53)   v2 = (0.82, 2.06, 0.76)  v3 = (-0.63, 2.06, 0.76)
   

2. distance between vertices:

   d1 =  1.125    d2 = 1.43   d3 = 1.46
   

3. distance between v3 and new vertice:

    d4 = 0.8
   

actually I know that this problem have two possible solutions

also I tried with the last equation and with some 2d equation, also I search in all thread of math stackenchage without any good result.

thanks for any help.

Diego

thanks to @Moti for help

Answer 1

It is not clear what you are trying to solve. You use d3 twice. Do you tey to calculate a distance?

The following diagram might help you define better your need:

CE is perpendicular to CB and in the same plane.