A triangle is defined by the points A(8,−5,3), B(1,−1,8), and C(−10,k,4). The area of the triangle is √(2116.25) Determine the value of k.

Answer 1

There are two real solutions as k appears in a quadratic equation as result of using inner product and

calculating length of base and height vector.

k=1 which as plausible answer confirms headed in right direction and the other value is k=117/37.

The video contains some 3 dimensional representation of the points and the associated triangle based upon one of solution in this case for k=1