Question

Three distinct points `P(3u^(2),2u^(3));Q(3v^(2),2v^(3))` and `R(3w^(2),2w^(3))` are collinear then

Answer 1

`|{:(3u^(2),,2u^(3),,1),(3y^(2),,2y^(3),,1),(3w^(2),,2w^(3),,1):}|=0`
`R_(1) to R_(1)-R_(2) " and " R_(2) to R_(2)-R_(3)`
`" or " |{:(u^(2)-v^(2),,u^(3)-v^(3),,0),(v^(2)-w^(2),,v^(3)-w^(3),,0),(w^(2),,w^(3),,1):}|=0`
`" or " |{:(u+v,,u^(2)+v^(2)+w,,0),(v+w,,v^(2)+w^(2),,0),(w^(2),,w^(3),,1):}|=0`
`R_(1) to R_(1)-R_(2)`
`" or " |{:(u-w,,(u^(2)-w^(2))+v(u-w),,0),(v+w,,v^(2)+w^(2)+vw,,0),(w^(2),,w^(3),,1):}|=0`
`" or " (v^(2)+w^(2)+vw)-(v+w)[(v+w)+u]=0`
`" or " v^(2)+w^(2)+vw-(v+w)^(2)-u (v+w) =0`
`" or " uv +vw +wu=0`