Points and are the vertices of a triangle in space

MATHEMATICS · Subjective · ISC · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

Points P(1,2,0),  Q(3,−1,4)P(1,2,0),\;Q(3,-1,4) and R(−2,1,5)R(-2,1,5) are the vertices of a triangle in space. (i) Find the Cartesian equation of the plane passing through the three points. (ii) Obtain a unit vector normal to this plane whose yy–component is negative.

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