Homework SourseFind the distance from the point S115 to the line L x1t y3t
Find the distance from the point S(1,1,5) to the line L: x=1+t, y=3-t, z=2t.
Solution
A (1,3,2) is a point on the line AS=2j-3k the line is parallel to v = i-j+2k/sqrt(6) projection of AS along the line = AS. v =(-2-6)/sqrt(6) =8/sqrt(6) |AS|=sqrt(0+4+9)=sqrt(13) so, distance= sqrt(|AS|^2 - 64/6) =sqrt(13-(64)/6)) =sqrt(14/6) =sqrt(7/3)
