Class XII Mathematics
Chapter 10: Three Dimensional Geometry
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Syllabus Sections
Key Formulas & Equations
Click Copy to duplicateLine Vector Equation
\vec{r} = \vec{a} + \lambda \vec{b}
Vector form of line passing through a parallel to b.
Shortest Distance Skew Lines
d = \frac{|(\vec{b}_1 \times \vec{b}_2) \cdot (\vec{a}_2 - \vec{a}_1)|}{|\vec{b}_1 \times \vec{b}_2|}
Distance between skew lines.
Related Formulas from Adjacent Chapters
Scalar Dot Product
\vec{a} \cdot \vec{b} = |a||b| \cos\theta
[From Vector Algebra] Computes scalar product of two vectors.
Vector Cross Product Magnitude
|\vec{a} \times \vec{b}| = |a||b| \sin\theta
[From Vector Algebra] Magnitude of cross product vector, representing bounded area.
Objective Function
Z = ax + by
[From Linear Programming] Target linear function optimized under boundary constraints.