i am given an equation of a line: [x,y,z]=[-3,-6,-11]+k[22,1,-11]
and i am being asked if it belongs to the plane defined by these three points A(2,5,6) B(-7,1,4) and C(6,-2,-9)
so first i calculated all three vectors between the points so i have AB=[-9,-4,2] AC=[4,-7,-15] BC=[13,-3,-13] and...