Find the equation of the plane through the points (2, 1, 0),
Question:

Find the equation of the plane through the points (2, 1, 0), (3, –2, –2) and (3, 1, 7).

Solution:

Given points are (2, 1, 0), (3, –2, –2) and (3, 1, 7)

As the equation of the plane passing through the points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) is

(x – 2) (-21) – (y – 1)(7 + 2) + z (3) = 0

-21 (x – 2) – 9(y – 1) + 3z = 0

-21x + 42 – 9y + 9 + 3z = 0

-21x – 9y + 3z + 51 = 0 ⇒ 7x + 3y – z – 17 = 0

Thus, the required equation of plane is 7x + 3y – z – 17 = 0.

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