1.

Find the equation of the plane passing through the point (2, -1, 3) and parallel to the plane E1 ≡ 3x + 4y - 7z + 5 = 0.

Answer»

Let E be the required plane. Since E is parallel to the plane E1 = 0, E is of the form

3x + 4y - 7z + d = 0

Since it passes through (2, -1,3), we have

3(2) + 4(-1) - 7(3) + d = 0 

d = 19

so E ≡ 3x + 4y - 7z + 19 = 0



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