Let O be the origin, and M and N be the points on the lines (x-5)/4=(y-4)/1=(z-5)/3 and (x+8)/12=(y+2)/5=(z+11)/9 respectively such that MN is the shortest distance between the given lines. Then O M · O N is equal to _ _ _ _ _.

Three Dimensional Geometry: JEE Main 2024 Mathematics question

JEE Main 2024 · 29 Jan, Evening shift · Q26

JEE Main 202429 Jan, Evening shiftMathematicsMediumThree Dimensional Geometry249× since 2002

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 _________.

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