Hi I wanted to check my work for this problem.
Consider the points A(1,0,0) B(2,2,2) and C(0,2,1).
1) Find the vector CA x CB
I got -2i -3j +4k for this
2) Find an exact value for the area of the triangle ABC.
I got sqrt29/2 for this.
3) Plane II(1) is 2x+3y-4z=2. A second plane II(2) is defined by the Cartesian equation II(2): 4x-y-z=4. Find the vector equation of L1: the intersection of the planes II(1) and II(2).
For this I got L1 = (0, 6, 8) + t(-1,-2,-2) by crossing the two planes, and then setting x to be 0? But I believe that this method might be wrong.
4) A third plane II(3) is defined by the Cartesian equation 16x + ay - 3z = b. Find the value of a if all three planes contain L1.
I got a = 4.
5) Find conditions on a and b if the plane II(3) does not intersect with L1.
I do not know how to tackle this problem at all.