Title Refresher Exam 1 Solution.pdf ✅

10. The plane is passing through the points A(-1, 2, 3) , B(-9, 8, -1) and C(2, 7, 10). Determine the equation of the plane. A. 22x + 18y – 14z + 74 = 0 C. x + 22y – 2z + 70 = 0 B. 31x + 22y – 29z + 74 = 0 D. 11x + 22y – 99z + 77 = 0 Form any two vectors using the three given points VBC =< (−9 − 2) (8 − 7) (−1 − 10) > = < −11 1 − 11 > VAC =< (−1 − 2) (2 − 7) (3 − 10) > = < −3 − 5 − 7 > Determine the cross product of the two vectors (It will be the normal vector of the plane) VBCxVAC =< −11 1 − 11 > x < −3 − 5 − 7 > VN =< −62 − 44 58 > The equation of the plane will be −62x − 44y + 58z + D = 0 Substitute any point to solve the constant −62(2) − 44(7) + 58(10) + D = 0 D = −148 −62x − 44y + 58z − 148 = 0 31x + 22y − 29z + 74 = 0