Posted by Krista on .
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,
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