Find the vector and Cartesian equation of the line passing through the point (1, 0,5) and is perpendicular to the line (x+2)/3 = (y-2)/4 = (z+3)/5 .

Also how wold solve these two equations:

l+2m+ 3n = 0

-3l+2m+5n = 0

The answer in my book is given as

l/10-6 = m/-9-5 = n/2+6

Here l,m,n are direction cosines.