Posted by Krista on .
Determine whether the planes are parallel or orthogonal.
5x - 3y + z = 4
x + 4y + 7z = 1
How exactly do I solve this? It wasn't covered completely in class.
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