# Math Help - planes in space

1. ## planes in space

could someone help me understand this? i have no idea how to answer it. the question is:
how can you tell when two places A1x +B1y +C1z=D1 and A2x+B2y+C2z=D2 are parallel? perpindicular? (the 1's and 2's are sub 1 and sub 2, i just don't know how to type that. if it makes any difference...)
if anyone could give me some help to clarify this it would be much appreciated. thanks.

2. Hi

One perpendicular vector to the first plane has coordinates $\left(A_1;B_1;C_1\right)$

One perpendicular vector to the second plane has coordinates $\left(A_2;B_2;C_2\right)$

The two planes are parallel when the two perpendicular vectors are collinear
In other words there exists k such that
$A_1 = k A_2$
$B_1 = k B_2$
$C_1 = k C_2$

By the way they are equal when also $D_1 = k D_2$

The two planes are perpendicular when the two perpendicular vectors are perpendicular
In other words when their dot product is equal to 0
$A_1 \times A_2 + B_1 \times B_2 + C_1 \times C_2 = 0$