Posted by **Krista** on Monday, April 8, 2013 at 10:47pm.

Determine whether the planes are parallel or orthogonal.

Equations given:

5x - 3y + z = 4

x + 4y + 7z = 1

How exactly do I solve this? It wasn't covered completely in class.

- Calculus -
**Reiny**, Tuesday, April 9, 2013 at 12:09am
The normals of the two planes are

(5, -3, 1) and (1 , 4, 7)

Since one is not a multiple of the other, the two planes cannot be parallel

if they are orthogonal (perpendicular) then their dot product must be zero

so (5,-3,1)∙(1,4,7) = 5 -12 + 7 = 0

YEs, they are orthogonal

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