Find the vector equation of the line which is parallel to the vector `3hati-2hatj+6hatk` and which passes through the point `(1,-2,3)`.

Explanation

Let `veca=3hati-2hatj+6hatk` and `vecb=hati-2hatj+3hatk`
so, vector equation of the line, which is parallel to the vector `veca=3hati-2hatj+6hatk` and passes through the vector `vecb=hati-2hatj+3hatk` is `vecr=vecb+lamdaveca`
`:. vecr=(hati-2hatj+3hatk)+lamda(3hati-2hatj+6hatk)`
`implies (xhati+yhatj+zhatk)-(hati-2hatj+3hatk)=lamda(3hati-2hatj+6hatk)`
`implies (x-1)hati+(y+2)hatj+(z-3)hatk=lamda(3hati-2hatj+6hatk)`