Question

Find the vector equation of the plane determined by the points (0,2,1),(2,1,0),(1,-1,0). Further, check whether the line r=(1+2α)I + (2-3α)j - (1+5α)k intersects this plane. If it intersects, find the point of intersection. If the line and plane do not intersects,find the equation of another line that intersects this plane

Answer 1

plane in parametric view

Plane:(0,2,1)+v(2-0,1-2,0-1)+u(1-0,-1-2,0-1)=(2v+u,2-v-3u,1-v-u)

1)1+2a=2v+u

2)2-3a=2-v-3u

3)-1-5a=1-v-u

3)2+5a=v+u

1)1+2a+2v+u=v+2+5a,v=-1-3a,u=3+8a

2)2-3a=2-(-1-3a)-3(3+8a),-3a=1-9+3a-24a ,-8=(24-3-3)a,a=-4/9.

line and plane intersect

point(1/9,10/3,11/9)