# planes in space

• Jan 26th 2010, 11:24 AM
isuckatcalc
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.
• Jan 26th 2010, 11:36 AM
running-gag
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
$A_1 \times A_2 + B_1 \times B_2 + C_1 \times C_2 = 0$