Question

if ax-bY=cz then x:y:z is:

Answer 1

The equation forms a straight line in 3d
$ax-by-cz=0$
$ax+(-b)y+(-c)z = 0$
it passes through origin (0,0,0)
we need one more point as (0,-c, b)
So we 2 point formula for line equation in 3d
[tex]r^{-} = r_{1}^{-} + t(r_{2}^{-} - r_{1}^{-} ) \\ r_{1}^{-} = 0 i + 0 j + 0 k \\ r_{2}^{-} = 0 i + (-c) j + bk \\ r^{-} = t(0 i + (-c) j + bk)\\ x = 0, y = -ct, z = bt \\ x:y:z = 0:-c:b [/tex]