Find the Cartesian equation of the plane passing through the points `A\ (0,0,0)` and `b(3,-1,2)` and parallel to the line `(x-4)/1=(y+3)/(-4)=(z+1)/7`

Explanation

Vector joining point `A` and `B` wil be,

`veca = 3hati-hatj+2hatk`

Given line is,

`(x-4)/1 = (y+3)/(-4) = (z+1)/7`

So, `vecb = hati-4hatj+7hatk` is the another vector in the plane.

So, a normal to the plane will be,

`vec a xx vec b`.

Now, `vec a xx vec b = |[hati,hatj,hatk],[3,-1,2],[1,-4,7]|`

...