The perpendicular distance from the origin to the plane containing the two lines, and , is

Engineering

Mathematics

Vector Product of Two Vectors

Distance from a Plane

Equation of Straight Line in 3D and Distance Of a Point From Line

Question

The perpendicular distance from the origin to the plane containing the two lines, $\frac{x + 2}{3} = \frac{y - 2}{5} = \frac{z + 5}{7}$ and $\frac{x - 1}{1} = \frac{y - 4}{4} = \frac{z + 4}{7}$ , is

$6 \sqrt{11}$

$\frac{11}{\sqrt{6}}$

$11 \sqrt{6}$

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$π : | \begin{matrix} x - 1 & y - 4 & z + 4 \\ 3 & 5 & 7 \\ 1 & 4 & 7 \end{matrix} | = 0$

π : 7x – 14y + 7z = – 77

π : x – 2y + z + 11 = 0

$p = | \frac{11}{\sqrt{1^{2} + 2^{2} + 1^{2}}} | = \frac{11}{\sqrt{6}}$