Question 1302d

Vectors II: Lines and Planes
Perpendicular Distance between Lines

Question

The line l{l} is given by
l1:r=(10−3)+λ(411),  λ∈R. l_1: \mathbf{r} = \begin{pmatrix} 1 \\ 0 \\ - 3 \end{pmatrix} + \lambda \begin{pmatrix} 4 \\ 1 \\ 1 \end{pmatrix}, \; \lambda \in \mathbb{R}.
Find the perpendicular distance between the line and the point B(1,2,4).{B \left( 1, 2, 4 \right).}

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