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Equation of a plane practice problems

A plane through three points, from a normal vector. 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.

Find an equation of the plane through the points \( \displaystyle (2, 1, -1),\ (-3, -3, 0),\ (2, -1, -1) \).
Problem 9.33medium✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-2, -1, -2),\ (2, 0, 3),\ (0, 0, 1) \).
Problem 9.40medium✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (0, 3, 3),\ (-3, 1, -1),\ (3, 0, -3) \).
Problem 9.44medium✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-2, 0, 3),\ (-2, 1, 1),\ (-2, -1, 2) \).
Problem 9.76medium✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-1, -3, 1),\ (-1, 2, 3),\ (-1, 0, 3) \).
Problem 9.81medium✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (0, 2, -1),\ (3, -1, 0),\ (-1, 3, 1) \).
Problem 9.82medium✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (3, -3, -3),\ (-3, 3, 1),\ (2, -2, 3) \).
Problem 9.87medium✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (0, 1, 0),\ (-1, 3, -2),\ (0, 2, 0) \).
Problem 9.88medium✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (1, 2, 3),\ (-1, -1, 3),\ (-1, 3, 0) \).
Problem 9.31hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (1, -1, 1),\ (-2, 1, 2),\ (0, -2, -3) \).
Problem 9.32hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (1, -2, 1),\ (-1, 1, 2),\ (-1, 3, 2) \).
Problem 9.34hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-3, -1, 1),\ (-1, 0, 0),\ (0, 0, -3) \).
Problem 9.35hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (1, -1, 3),\ (3, 1, 0),\ (2, 1, 3) \).
Problem 9.36hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-2, 1, -1),\ (-3, 3, 1),\ (-1, 3, 3) \).
Problem 9.37hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-2, -2, -1),\ (1, -1, -1),\ (-1, -2, -3) \).
Problem 9.38hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-1, -2, 0),\ (-3, 3, 2),\ (0, 0, -3) \).
Problem 9.39hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (3, 3, -3),\ (-2, 2, -3),\ (-2, -3, -1) \).
Problem 9.41hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-2, 0, 3),\ (-3, 3, -3),\ (1, 3, -3) \).
Problem 9.42hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (2, 0, -1),\ (-2, 1, 2),\ (3, -2, -2) \).
Problem 9.43hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (2, 0, -1),\ (2, -3, 1),\ (-2, 3, 2) \).
Problem 9.45hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-3, 0, 0),\ (-3, 3, -2),\ (3, -2, 2) \).
Problem 9.77hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (0, 1, 0),\ (-2, -1, 3),\ (3, -1, -2) \).
Problem 9.78hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-1, 2, 2),\ (-3, -1, 3),\ (2, -2, -2) \).
Problem 9.79hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-2, -1, -2),\ (-3, 2, 2),\ (1, -1, 1) \).
Problem 9.80hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-2, 2, -3),\ (0, 2, -2),\ (-2, -1, 0) \).
Problem 9.83hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-1, 0, 0),\ (0, -3, -1),\ (-2, 0, -1) \).
Problem 9.84hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (1, 1, 2),\ (0, 3, 3),\ (1, -2, 3) \).
Problem 9.85hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-3, 3, -3),\ (1, 2, -2),\ (2, -3, 1) \).
Problem 9.86hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (2, -2, -2),\ (-2, -1, -2),\ (1, -3, 1) \).
Problem 9.89hard✓ Every equation proved
Find an equation of the plane through the points \( \displaystyle (-1, 3, -1),\ (1, 1, 0),\ (0, -3, -3) \).
Problem 9.90hard✓ Every equation proved