When Is a Vector Parallel to a Plane?

Two planes are parallel if their normal vectors are parallel (constant multiples of one another). It is easy to recognize parallel planes written in the form ax+by+cz=d since a quick comparison of the normal vectors n=<a,b,c> can be made.

How do you know if a vector is parallel to a plane?

To find a vector parallel to the plane we need only find two points which lie on the plane. As these two points lie on the plane, →v lies on the plane, and is therefore parallel to it.

How do you check whether a line is parallel to a plane?

A line is parallel to a plane if the direction vector of the line is orthogonal to the normal vector of the plane. To check whether two vectors are orthogonal, you can find their dot product, because two vectors are orthogonal if and only if their dot product is zero.