Question

a plane is perpendicular to both [x,y,z]=[1,-10,8]+s[1,2,-1] and [x,y,z]=[2,5,-5]+t[2,1,-3] and contains the point P(-1,4,-2). Determine if the point A(7,10,16) is also on the plane.

Answer 1

cross your direction vectors to get the normal; then apply the given point to it, then see of the questionable point fits the equation

Answer 2

i always tend to misread perp and parallel

Answer 3

unless the direction vectors are scalars of one another, i dont see a plane being perp to both

Answer 4

now if its parallel to both lines, then the direction vectors can be part of the plane, and a normal can be determined by a cross