SOLUTION: Find all values of k such that the triangle in R3 with vertices A(1,3,-1), B (0,5,-2), C(k,3,1) is a right angle triangle

Algebra ->  Vectors -> SOLUTION: Find all values of k such that the triangle in R3 with vertices A(1,3,-1), B (0,5,-2), C(k,3,1) is a right angle triangle       Log On


   

Question 1043770: Find all values of k such that the triangle in R3 with vertices
A(1,3,-1), B (0,5,-2), C(k,3,1) is a right angle triangle
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Slope AB, %28-1-%28-2%29%29%2F%281.3-0.5%29=-1%2F0.8=-10%2F8=highlight_green%28-5%2F4%29

Slope AC, %283.1%2B1%29%2F%28k-1.3%29=highlight_green%284.1%2F%28k-1.3%29%29

Slope BC,%283.1%2B2%29%2F%28k-0.5%29=highlight_green%285.1%2F%28k-0.5%29%29


Slopes m%5Bh%5D and m%5Bj%5D of perpendicular lines are related as m%5Bh%5Dm%5Bj%5D=-1. You can make three such equations using your slopes; and solve each for k.