Three dimensional geometry Topics - IIT JEE Syllabus

1

2m1/10

📌 Key Formula(x, y, z) coordinates in 3D.

2

2m1/10

📌 Key FormulaDistance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

3

2m2/10

📌 Key FormulaInternal division: ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n), (mz₂ + nz₁)/(m+n))

4

2m2/10

📌 Key Formulal² + m² + n² = 1, direction ratios a, b, c proportional to l, m, n: l/a = m/b = n/c = ±1/√(a²+b²+c²)

5

2m2/10

📌 Key Formulacos θ = |l₁l₂ + m₁m₂ + n₁n₂|

6

2m2/10

📌 Key FormulaLines not parallel and not intersecting.

7

2m5/10

📌 Key FormulaShortest distance between skew lines = |(b₁×b₂)·(a₂ - a₁)| / |b₁×b₂|

8

2m3/10

📌 Key FormulaVector form: r = a + λb, Cartesian: (x - x₁)/l = (y - y₁)/m = (z - z₁)/n

9

2m3/10

📌 Key FormulaSolve line and plane equations together to get point of intersection.

10

2m4/10

📌 Key FormulaCondition: (a₂ - a₁)·(b₁×b₂) = 0

11

2m2/10

📌 Key Formulaax + by + cz + d = 0

12

2m2/10

📌 Key FormulaDistance = |ax₁+by₁+cz₁+d|/√(a²+b²+c²)