The distance between the line and the plane is

MATHEMATICS · Single correct · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

The distance between the line r=2i−2j+3k+λ(i−j+4k)\mathbf{r} = 2\mathbf{i} - 2\mathbf{j} + 3\mathbf{k} + \lambda(\mathbf{i} - \mathbf{j} + 4\mathbf{k}) and the plane r⋅(i+5j+k)=5\mathbf{r} \cdot (\mathbf{i} + 5\mathbf{j} + \mathbf{k}) = 5 is (1) 1033\frac{10}{3\sqrt{3}} (2) 103\frac{10}{3} (3) 109\frac{10}{9} (4) 103\frac{10}{\sqrt{3}}

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