JC
JC H2 Math: Vectors—A Fast Method for Lines, Planes and Shortest Distance
•By Intuitional Team•1 min read
Turn geometry pictures into vector equations quickly, then apply dot/cross product identities to compute distances cleanly.
Representation
Parametric line: r = a + λb. Plane: r ⋅ n = d. Two planes intersect in a line parallel to n₁ × n₂.
Shortest distance
- Point–line: |(AP × b)| / |b|.
- Point–plane: |r₀ ⋅ n − d| / |n|.
- Skew lines: project the connector on (b₁ × b₂).
Exam routine
- Sketch and label vectors.
- Write the algebraic form cleanly.
- Use identities: a⋅(b×c)=b⋅(c×a) to simplify.
Always conclude with a sentence interpreting the result (units, direction, or locus).
Tags
JCH2 MathVectorsPlanesDistanceGeometry