Find the vector equation of the line passing through (1,2,3) and parallel to the planes `vecr.(hati-hatj+2hatk)=5` and `vecr.(3hati+hatj+hatk)=6`.

Explanation

Line is parallel to the planes `vecr*(hati-hatj+2hatk)=5 and vecr*(3hati+hatj+hatk)=6`, i.e., line is perpendicular to the vectors `hati-hatj+2hatk and 3hati+hatj+hatk`
`therefore` Line is parallel to the vector `(hati-hatj+2hatk)xx(3hati+hatj+hatk)=|{:(hati,,hatj,,hatk),(1,,-1,,2),(3,,1,,1):}|=-3hati+5hatj+4hatk`
Line passes through (1, 2, 3).
`therefore` Equation of line is `vecr=(hati+2hatj+3hatk)+lamda(-3hati+5hatj+4hatk)`