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In: Advanced Math

A plane in R3 can be given by an equation Ax + By + Cz =...

A plane in R3 can be given by an equation Ax + By + Cz = D where A, B, C, and D areconstants and A, B, and C are not all zero. Suppose two planes are given by equations A1x+B1y+C1z = D1 and A2x+B2y+C2z = D2. The intersection of the two planes can be empty, or it can be a line, or the planes could be identical. How can the correct possibility be determined from the constants in the equations? Explain! (Hint: Think in terms of solving linear systems.)

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