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

My thinking is, n=[1,2-1]x[2,1,-3] and this vector "n" will be perpendicular to the two lines and parallel to the said plane containing point "P". IF "A" is also in the said plane, then vector APxn will be a vector coplanar to the plane spanned by the direction vectors of the original two lines given. This is indeed what happens. But the textbook says, "No, point A is not also on this plane. Any comments?