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2. Let P 1 and P2 be planes with general equations P1 : −2x + y...

2. Let P 1 and P2 be planes with general equations P1 : −2x + y − 4z = 2, P2 : x + 2y = 7.

(a) Let P3 be a plane which is orthogonal to both P1 and P2. If such a plane P3 exists, give a possible general equation for it. Otherwise, explain why it is not possible to find such a plane. (b) Let ` be a line which is orthogonal to both P1 and P2. If such a line ` exists, give a possible vector equation for it. Otherwise, explain why it is not possible to find such a line.

Thanks!

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