Q.30. Find the length of the perpendicular drawn from the point P3, 2. 1) to the anc i=( 7i + 7i + 6i ,)+ beta i (-2i+2i+3 tilde k ]

The problem requires finding the length of the perpendicular drawn from the point \( P(3, 2, 1) \) to the given line. The line is defined by a vector equation.

Given:
- Point \( P(3, 2, 1) \)
- The line is represented as:  
  \[
  \mathbf{r} = \mathbf{a} + \lambda \mathbf{b}
  \]
  where \( \mathbf{a} = 7\mathbf{i} + 7\mathbf{j} + 6\mathbf{k} \) and \( \mathbf{b} = -2\mathbf{i} +

Discover how to calculate the perpendicular distance from point (3, 2, 1) to a line defined in 3D space. This problem involves understanding vector equations of lines and applying the distance formula in 3D geometry. Suitable for advanced high school students.

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