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Find the distance of point (2, 0, 1) fro...

Find the distance of point (2, 0, 1) from the line whose symmetric equations are
`(x-2)/3=(y+1)/4=(z-1)/(-2)`.

Text Solution

Verified by Experts

Distance of line from a given point
`=abs((vec(PA)xx(ahati+bhatj+chatk))/(abs(ahati+bhatj+chatk)))`
here `vec(PA)=hatj`
`ahati+ bhatj +c hatk =3hati + 4hatj-2hatk`
so distance will be
`=abs((hatj xx (3hati +4hatj-2hatk))/(sqrt(9+16+4)))`
`=abs((-3hatk-2hati)/(sqrt(29)))= sqrt(13/29)`
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