Class XII Mathematics

Chapter 10: Three Dimensional Geometry

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Key Formulas & Equations

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Line Vector Equation

A(x₁, y₁)B(x₂, y₂)d
\vec{r} = \vec{a} + \lambda \vec{b}

Vector form of line passing through a parallel to b.

Shortest Distance Skew Lines

sin θcos θθ
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.