(Solution) - a Show that the graph of an equation of the -(2025 Original AI-Free Solution)

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(a) Show that the graph of an equation of the form given in (10), with a, b, and c not all zero, is a plane with normal v = ai + bj + ck.
(b) Show that the set of all points on the plane ax + by + cz = 0 is a subspace of R3.
(c) Find a basis for the subspace given by the plane 2x - 3y + 4z = 0.