JEE Main allocates 3-4 questions to 3D geometry annually. Distribution: shortest distance between lines (20%), equation of plane (20%), distance from point to plane/line (15%), angle problems (15%), image/reflection (15%), coplanarity and intersection (15%).
Most common PYQ type: "Find the shortest distance between two given lines." This directly applies the formula SD = |[a2-a1, b1, b2]|/|b1 x b2|. The computation requires a 3x3 determinant and a cross product.
Second most common: "Find the equation of a plane satisfying conditions." The family-of-planes approach (P1+lambda*P2=0) is the most efficient method when the plane passes through the intersection of two given planes.
Third type: "Find the image of a point/line in a plane." Follow the perpendicular-foot-image algorithm systematically.
Numerical answer type: Often asks for distances (exact values), angles (in terms of inverse trig), or parameter values (for coplanarity or perpendicularity conditions).
Key formulas to have ready:
- Distance from point to plane: |ax0+by0+cz0-d|/sqrt(a^{2+b}^{2+c}^2)
- Shortest distance: |scalar triple product|/|cross product|
- Distance from point to line: |AP x b|/|b|
- Line-plane angle: sin(theta)=|b.n|/(|b||n|)
- Coplanarity: scalar triple product = 0
- Image formula: 2*foot - point
Time management: 3D problems typically take 3-5 minutes. The cross product and determinant computations are the bottleneck. Practice these to speed up.