Saitechinfo CBSE NEET JEE Academy - 3D Geometry Checklist

3D Geometry Topic Tree

Track your preparation for CBSE, NEET, and JEE.

Direction Cosines (l, m, n)

Relation: l² + m² + n² = 1

Direction Ratios

Proportional numbers to DC's

Line passing through two points

Finding DC's of the line connecting P(x1,y1,z1) and Q(x2,y2,z2)

Equation: Point & Parallel Vector

Vector form: r = a + λb

Equation: Passing through 2 Points

Vector form: r = a + λ(b - a)

Angle between Two Lines

Using dot product of direction vectors

Shortest Distance: Skew Lines

Non-parallel, non-intersecting lines

Shortest Distance: Parallel Lines

Using cross product formula

Equation: Normal Form

lx + my + nz = d

Equation: Point & Normal Vector

(r - a) . N = 0

Equation: 3 Non-Collinear Points

Determinant form or (r-a).[(b-a)x(c-a)] = 0

Intercept Form

x/a + y/b + z/c = 1

Intersection of Two Planes

Family of planes: P1 + λP2 = 0

Coplanarity of Two Lines

Condition for two lines to lie on same plane

Angle between Two Planes

Angle between their normal vectors

Distance of a Point from a Plane

Perpendicular distance formula

Angle between Line and Plane

Complement of angle between line and normal