Strategy 1 -- Direction identification: Always extract DRs from given information first. For lines between two points: subtract coordinates. For intersection of two planes: cross product of normals. For perpendicular to a plane: read off the normal.
Strategy 2 -- Choose the right formula: Distance from point to plane (direct formula). Distance from point to line (cross product). Shortest distance between lines . Don't derive -- apply directly.
Strategy 3 -- Family of planes: When "plane through intersection of two planes" appears, immediately write P1+lambda*P2=0 and determine lambda from the additional condition. This avoids finding the intersection line explicitly.
Strategy 4 -- Coplanarity check: For two lines, compute the scalar triple product determinant. Zero = coplanar. Non-zero = skew, and the determinant's absolute value divided by |b1 x b2| gives the shortest distance.
Strategy 5 -- Image and reflection: Follow the systematic algorithm: write perpendicular line, find foot, compute image. Don't try to guess the image point.
Strategy 6 -- Angle computation: For line-line angle, use the dot product formula with DRs. For plane-plane, same formula with normals. For line-plane, use sin(theta) = |b.n|/(|b|*|n|). Remember: line-plane angle involves sine, not cosine.
Common traps: (1) Forgetting absolute value in angle formulas (getting obtuse instead of acute). (2) Using cos for line-plane angle instead of sin. (3) Not normalizing DRs when using direction cosine formulas. (4) Confusing the shortest distance formula for skew lines with the parallel lines formula.