`y=z+(1)/(1+(1)/(x))`

If y is the H.M. between x and z, prove that, (1)/(y-x) + (1)/(y-z) = (1)/(x) + (1)/(z) .

Solve : (1)/(2x)+(1)/(4y)-(1)/(3z)=(1)/(4),(1)/(x)=(1)/(3y),(1)/(x)-(1)/(5y)+(4)/(z)=2 (2)/(15)

Shortest distance between the lines (x-1)/(1) = (y-1)/(1) = (z-1)/(1) and (x-2)/(1) = (y-3)/(1) = (z-4)/(1) is equal to

Show that the lines (x-1)/(1) = (y-2)/(-1) = (z-1)/(1) and (x-1)/(1-) = (y-1)/(-1) = (z-1)/(2) do not intersect.

Show that the lines (x-1)/(1) = (y-2)/(-1) = (z-1)/(1) and (x-1)/(1-) = (y-1)/(-1) = (z-1)/(2) do not intersect.

Equation of a line in the plane pi =2x-y+z-4=0 which is perpendicular to the line l whose equation is (x-2)/1=(y-2)/(-1)=(z-3)/(-2) and which passes through the point of intersection of l and pi is (A) (x-2)/1=(y-1)/5=(z-1)/(-1) (B) (x-1)/3=(y-3)/5=(z-5)/(-1) (C) (x+2)/2=(y+1)/(-1)=(z+1)/1 (D) (x-2)/2=(y-1)/(-1)=(z-1)/1

Equation of a line in the plane pi =2x-y+z-4=0 which is perpendicular to the line l whose equation is (x-2)/1=(y-2)/(-1)=(z-3)/(-2) and which passes through the point of intersection of l and pi is (A) (x-2)/1=(y-1)/5=(z-1)/(-1) (B) (x-1)/3=(y-3)/5=(z-5)/(-1) (C) (x+2)/2=(y+1)/(-1)=(z+1)/1 (D) (x-2)/2=(y-1)/(-1)=(z-1)/1

Equation of a line in the plane pi =2x-y+z-4=0 which is perpendicular to the line l whose equation is (x-2)/1=(y-2)/(-1)=(z-3)/(-2) and which passes through the point of intersection of l and pi is (A) (x-2)/1=(y-1)/5=(z-1)/(-1) (B) (x-1)/3=(y-3)/5=(z-5)/(-1) (C) (x+2)/2=(y+1)/(-1)=(z+1)/1 (D) (x-2)/2=(y-1)/(-1)=(z-1)/1