Question 1302d

Vectors II: Lines and Planes
Perpendicular Distance between Lines

Question

The line l{l} is given by
l1:r=(5−3−5)+λ(−412),  λ∈R. l_1: \mathbf{r} = \begin{pmatrix} 5 \\ - 3 \\ - 5 \end{pmatrix} + \lambda \begin{pmatrix} - 4 \\ 1 \\ 2 \end{pmatrix}, \; \lambda \in \mathbb{R}.
Find the perpendicular distance between the line and the point B(5,2,5).{B \left( 5, 2, 5 \right).}

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