Determine whether the given planes are the same. 5(x + 2) + (y - 9) + 7(z + 7) = 0
5(x + 3) + (y - 6) + 7(z - 6) = 0
A) The planes are the same.
B) The planes are not the same.

Question

Quizplus · Accepted Answer

The planes are not the same. To see this, we can expand both equations:

5(x + 2) + (y - 9) + 7(z + 7) = 0
5x + 10 + y - 9 + 7z + 49 = 0
5x + y + 7z + 50 = 0

5(x + 3) + (y - 6) + 7(z - 6) = 0
5x + 15 + y - 6 + 7z - 42 = 0
5x + y + 7z - 33 = 0

We can see that the two equations are not equivalent, since the constants are different.

Determine Whether the Given Planes Are the Same