If Ā = 2i -3j + k and B= -i + 4j -2k are normals of the two planes, do the planes necessary intersect ? give the reason. If they intersect find a vector parallel to their line of intersection.

Question

If  Ā = 2i -3j + k  and  B= -i + 4j -2k  are normals of the two planes,  do the planes necessary intersect ? give the reason. If they intersect find a vector parallel to their line of intersection.

hartnn · Answer

if the 2 planes are parallel, their normals are also parallel, so you just need to check whether A and B are parallel.
if they are, then they are not intersecting...

klimenkov · Answer

If these vectors are not parallel, then the planes intersect. And the vector of the line of the intersection will be the vector product of the normals of the planes.