Show that the Vector u 1 2 3 is perpendicular to every vect

Show that the Vector u = [1, 2, 3} is perpendicular to every vector on the plane 2x+4y+6z=12.

Solution

equation of plane is
2x + 4y + 6z =12

so the normal vector to the plane is <2,4,6>

so, any vector than can be written as <2,4,6> my multiplying and dividing by an integer is parallel to normal vector

(1,2,3) = 0.5*<2,4,6>

so, (1,2,3) is parallel to normal vector

Hence it is also normal to the plane

proved