Points A, B, C have coordinates (1, 2, 1), (1, 1, 3) and (2, 2, 2)

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Points A, B, C have coordinates (1, 2, 1), (–1, 1, 3) and (–2, –2, –2) respectively. Calculate the vector product AB(vector) × AC(vector), the angle BAC and a unit vector perpendicular to the plane containing A, B and c. Hence obtain

(a) The equation of the plane ABC;

(b) The equation of a second plane, parallel to ABC, and containing the point D(1, 1, 1);

(c) The shortest distance between the point D and the plane containing A, B and C.

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