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3D Geometry question

2024 · 29 Jan · Shift 2 · Q51

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JEE Main
Mathematics
3D Geometry
2024 · 29 Jan · Shift 2 · Q51

3D Geometry question

2024 · 29 Jan · Shift 2 · Q51

JEE MainMathematics3D GeometryNumerical+4 / −1

Let O be the origin, and M and

\mathrm{N}

be the points on the lines

\frac{x-5}{4}=\frac{y-4}{1}=\frac{z-5}{3}

and

\frac{x+8}{12}=\frac{y+2}{5}=\frac{z+11}{9}

respectively such that

\mathrm{MN}

is the shortest distance between the given lines. Then

\overrightarrow{O M} \cdot \overrightarrow{O N}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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