Find the equation of the plane which is parallel to the lines ` vec r= hat i+ hat j+lambda(2 hat i+ hat j+4 hat k)a n d(x+1)/(-3)=(y-3)/2=(z+2)/1""` and is passing through the point `(0,1,-1` ).

Explanation

The plane is parallel to the given lines, which are directed along vectors `veca=2hati+hatj+4hatk and vecb=-3hati+2hatj+1hatk`.
Then the plane is normal to vector `vecaxxvecb-=|{:(hati,,hatj,,hatk),(2,,1,,4),(-3,,2,,1):}|=-7hati-14hatj+7hatk`
Also, the plane passes through the point (0, 1, -1)
Therefore, the equation of the plane is `-7(x-0)-14(y-1)+7(z+1)=0 or 7x+14y-7z=21`