Find the equation of the line passing through the intersection `(-1,2,3)` and perpendicular to the lines `(x-1)/2=(y-2)/(-3)=(z-3)/4a n d(x-4)/5=(y-1)/2=zdot` and also through the point `(2,1,-2)dot`

Explanation

Intersection point of the lines
`" "(x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=z`
is (-1, -1, -1) (on solving). Therefore, the equation of the line passing through the points(-1, -1, -1) and (2, 1, -2) is `(x+1)/(3)=(y+1)/(2)=(x+1)/(-1)`.