Describe the solution set of the ff cases, given the linear system a_1x + b_1y + c_1z = d_1 (Plane 1) a_2x + b_2y + c_2z = d_2 (Plane 2) a_3x + b_3y + c_3z = d_3 (Plane 3) (a) The 3 planes are parallel and distinct. (b) The 3 planes coincide. (c) Plane 1 and Plane 2 coincide and are parallel to Plane 3.

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Describe the solution set of the ff cases, given the linear system
a_1x + b_1y + c_1z = d_1 (Plane 1)
a_2x + b_2y + c_2z = d_2 (Plane 2)
a_3x + b_3y + c_3z = d_3 (Plane 3)

(a) The 3 planes are parallel and distinct.
(b) The 3 planes coincide.
(c) Plane 1 and Plane 2 coincide and are parallel to Plane 3.
(d) Plane 1 and Plane 2 intersect in a line L that is parallel to Plane 3.
(e) Plane 1 and Plane 2 intersect in a line L that lies in Plane 3.
(f) Plane 1 and Plane 2 intersect in a line L that intersects Plane 3 in a single point.

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