Find the scalar equation of the plane that passes through the point (4, 1, 3) and is parallel to the xy-plane.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to remember that two planes are parallel if the normal vectors to these planes are parallel.

The problem provides the information that the plane `P_1`  passes through the point (4,1,3), hence you may write the scalar equation of plane such that:

`a(x - 4) + b(y - 1) + c(z - 3) = 0`

a,b,c express the coefficients of normal vector `bar n_1`  to the plane `P_1` .

You shoud remember that the scalar equation of xy plane is z=0 , hence the normal vector `bar n_2`  is `bar k = bar n_2` .

You need to set `bar n_1`  equal to `bar n_` 2 such that:

`k(z - 3) = 0 =gt kz - 3k = 0 =gt`  kz = 3k => z = 3

Hence, evaluating the scalar equation of the plane passing through the point (4,1,3) and parallel to xy plane yields z = 3.