Calculus

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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 -

    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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