**3-D Geometry **

**Direction Angle (θ):**

- The direction angle of a line is the angle it makes with a coordinate axis.
- Direction angles (α, β, γ) can be calculated using trigonometric functions:

**Direction Cosines (l, m, n):**

- Direction cosines are the cosines of the angles a line makes with the coordinate axes.
- They are represented as (l, m, n).
- Example: For a line with direction angles (α, β, γ), direction cosines are (cos(α), cos(β), cos(γ)).

**Direction Ratios (a, b, c):**

- Direction ratios (a, b, c) are proportional to direction cosines and represent the ratio of lengths along the axes.
- Example:

**Relation between Direction Cosines and Direction Ratios:**

- Direction cosines (l, m, n) are obtained by dividing direction ratios (a, b, c) by the magnitude of the line.
- Example: l = a/|OP|, m = b/|OP|, n = c/|OP|, where OP is the vector representing the line.

**Equation of Line: Line Passing Through a Given Point in a Given Direction:**

- Vector form: r = a + λb, where 'a' is a point on the line, 'b' is the direction vector, and 'λ' is a parameter.
- Cartesian form: (x - x
_{1})/a = (y - y_{1})/b = (z - z_{1})/c.

**Equation of Line: Line Passing Through Two Points:**

- Vector form: r = a + λ(b - a), where 'a' and 'b' are two points on the line, and 'λ' is a parameter.
- Cartesian form can be derived from vector form.

**Angle Between Two Lines (θ):**

To be continue...

**Shortest Distance Between Skew and Parallel Lines:**

To be continue....