JEE Main Mathematics

Three-Dimensional Geometry

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JEE Main Mathematics

Three-Dimensional Geometry

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Points in space, direction cosines and ratios, the angle between two lines, the equation of a line, and the shortest distance between skew lines.

Key formula

\cos\theta = \frac{|a_1a_2 + b_1b_2 + c_1c_2|}{\sqrt{a_1^2 + b_1^2 + c_1^2}\,\sqrt{a_2^2 + b_2^2 + c_2^2}}, \quad d = \frac{|(\vec{a}_2 - \vec{a}_1) \cdot (\vec{b}_1 \times \vec{b}_2)|}{|\vec{b}_1 \times \vec{b}_2|}

What this unit covers

Coordinates of a point in space, the distance between two points, section formula
Direction ratios and direction cosines
The angle between two intersecting lines
Equation of a line
Skew lines, the shortest distance between them and its equation