Math intersection of planes
posted by Shaila .
Show that the line [x,y,z]=[10,5,16]+t[3,1,5] is contained in the plane x+2yz4=0
I tries writing the vector equation in parametric form and then substituting it into the respective x,y,z in the plane, after simplifying I get 0t=0 does this mean that the line is in the plane or did I do something wrong

Yes, that means that the line is in the given plane.
You can also take any two distinct points on the given line (i.e. two arbitrary values of t) and prove that each of the point lies in the plane.