The distance of a point A−$$2$$,$$3$$,$$1$$ from the line MN→ throughM−$$3$$,$$5$$,$$2$$ , which makes equal angles with the coordinate axes is

Question

The distance of a point A−$$2$$,$$3$$,$$1$$ from the line  MN→ throughM−$$3$$,$$5$$,$$2$$ , which makes equal angles with the coordinate axes is

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The equation of line passing through M−$$3$$,$$5$$,$$2$$ and making equal angles with coordinate axes is $$x+31=y$$−$$51=z$$−$$21General$$ point on the above line isPk−$$3$$,$$k+5$$,$$k+2If$$ the perpendicular distance from  A−$$2$$,$$3$$,$$1$$ to the above line is AP  then  APis perpendicular to the line  $$x+31=y$$−$$51=z$$−$$21Hence$$, k−$$1$$⋅$$1+k+2$$⋅$$1+k+1$$⋅$$1=03k+2=0k=$$−$$23$$ Hence the point  Pk−$$3$$,$$k+5$$,$$k+2$$ is P−$$113$$,−$$135$$,−$$43The$$ required distance is AP,  $$AP=259+169+19=143$$

The distance of a point $A (- 2, 3, 1)$ from the line $\vec{M N}$ through $M (- 3, 5, 2)$ , which makes equal angles with the coordinate axes is

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The distance of a point A−2,3,1 from the line MN→ throughM−3,5,2 , which makes equal angles with the coordinate axes is

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The distance of a point $A (- 2, 3, 1)$ from the line $\vec{M N}$ through $M (- 3, 5, 2)$ , which makes equal angles with the coordinate axes is