Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane ` -> rdot( hat i+2 hat j-5 hat k)+9=0` .

Explanation

Given plane is `vecr. (hati+2hatj-5hatk) + 9 = 0`
Its cartesian equation is `x+2y-5z+9=0`
The direction ratios of line perpendicular to plane are ` (1,2,-5)` . If this line passes through the point (1,2,3) then equation of line is
`(x-1)/(1) = (y-2)/(2) = (z-3)`
The vector form of this equation is,
`vecr= (hati+2hatj+3hatk) + lambda(1hati+2hatj-5hatk)`
where `lambda` is a real number.