Find a plane containing the point (-7,-6,1) and the line r(t)=(2,8,3)+t(7,3,-2)

Answer 1

1) define point Q on the line = <2,8,3>

2) define line PQ=<2,8,3>+t<2+7,8+6,3-1> = <2,8,3>+t<9,14,2>

3) define L1 (giiven) = <2,8,3>+t<7,3,-2>

4) 2 intersecting lines define a plane thus PQXL1 = N (plane normal)

5) In 4, use only the direction vector components of PQ and L1

6) Find N to be <-34,-32,-21>

7) Find the plane equation to be -34x-32y-21z=D

8) Find D by setting using point (2,8,3) = -387

9) Equation of plane is 34x+32y+21z=387