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Projection of a line on axis are −3,4,−1...

Projection of a line on axis are `−3,4,−12`. Find length of line segment and direction cosines.

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The given line is `(x-3)/(2)=(y+1)/(-2)=(z-3)/(5)`
Note that it passes through (3, -13) and is parallel to the line whose direction ratios are 2, -2 and 5. Therefore, its vector equation is `vecr=3hati-hatj+3hatk+lamda(2hati-2hatj+5hatk)`, where `lamda` is a parameter.
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