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By computing the shortest distance, determine whether following lines intersect each other.

\(\frac{x - 5}{4} = \frac{y - 7}{-5} = \frac{z + 3}{-5}\) and \(\frac{x - 8}{7} = \frac{y - 7}{1} = \frac{z - 5}{3}\)

(x - 5)/4 = (y - 7)/-5 = (z + 3)/-5 and (x - 8)/7 = (y - 7)/1 = (z - 5)/3

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(x - 5)/4 = (y - 7)/-5 = (z + 3)/-5 and (x - 8)/7 = (y - 7)/1 = (z - 5)/3

The shortest distance between the lines

 \(\frac{x - 5}{4} = \frac{y - 7}{-5} = \frac{z + 3}{-5}\) and \(\frac{x - 8}{7} = \frac{y - 7}{1} = \frac{z - 5}{3}\) is given n by

The equation of the given lines are

Hence, the required shortest distance between the given lines

or

The shortest distance between the lines \(= \frac{282}{\sqrt{3830}}\) units

Hence, the gives lines do not intersect.

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