( 717, #59 ) Which of the following four planes are parallel

( 717, #59 ) Which of the following four planes are parallel? Are any of them identical?

Solution: The planes

are parallel if and only if

< a, b, c > = k < A, B, C >
for some constant k.
The planes are identical if and only if the planes are parallel and

d = k*D .
The two planes are parallel because they are proportional to each other by the constant
k = -3/2.
The two planes are parallel because they are proportional to each other by the constant k = 2. The planes are also identical because their 'd' values are also proportional by the constant
k = 2.

by: nl