Lines and Planes in Space

Applied Mathematics — Second Secondary

Common mistakes

Comparison aspect	Main idea	Keywords
Mistake	deciding that two lines are parallel because they do not meet in the drawing. Correct: skew lines do not meet and are not parallel so check whether they lie in one plane	decidinglinesparallelbecause
Mistake	proving that a line is perpendicular to a plane from its perpendicularity to a single line in the plane. Correct: the line must be perpendicular to two intersecting lines in the plane	provinglineperpendicularplane
Mistake	taking the angle between the diagonal and the plane to be the angle between the diagonal and an edge. Correct: the required angle is between the diagonal and its perpendicular projection on the plane	takinganglebetweendiagonal
Mistake	using the edge length in place of the diagonal. Correct: the space diagonal of a cube equals the edge × √3 not the edge itself or twice the edge	usingedgelengthplace

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