If a vector equation involves parameters, then it is called a vector equation in  Cartesian equationcoplanarnon–parametric formnormal to the planeparametric formperpendicularscalar triple productshortest distanceskew linesvector triple product.

If no parameter is involved,then the equation is called a vector equation in  Cartesian equationcoplanarnon–parametric formnormal to the planeparametric formperpendicularscalar triple productshortest distanceskew linesvector triple product.

Two lines are said to be  Cartesian equationcoplanarnon–parametric formnormal to the planeparametric formperpendicularscalar triple productshortest distanceskew linesvector triple product if they lie in the same plane.

Two lines in space are called  Cartesian equationcoplanarnon–parametric formnormal to the planeparametric formperpendicularscalar triple productshortest distanceskew linesvector triple product if they are not parallel and do not intersect .

A straight line which is perpendicular to a plane is called a  Cartesian equationcoplanarnon–parametric formnormal to the planeparametric formperpendicularscalar triple productshortest distanceskew linesvector triple product.

For a given set of three vectors a̅ ,b̅ and c̅ , the scalar(a̅×b̅).c̅ is called a  Cartesian equationcoplanarnon–parametric formnormal to the planeparametric formperpendicularscalar triple productshortest distanceskew linesvector triple product of a̅ ,b̅ , c̅.

The scalar triple product of three non-zero vectors is zero if and only if the three vectors are  Cartesian equationcoplanarnon–parametric formnormal to the planeparametric formperpendicularscalar triple productshortest distanceskew linesvector triple product.

For a given set of the scalar(a̅×b̅)×c̅ is called a  Cartesian equationcoplanarnon–parametric formnormal to the planeparametric formperpendicularscalar triple productshortest distanceskew linesvector triple product of a̅ ,b̅ , c̅.

 Cartesian equationcoplanarnon–parametric formnormal to the planeparametric formperpendicularscalar triple productshortest distanceskew linesvector triple product of the plane in normal form is lx +my+ nz =p.

The  Cartesian equationcoplanarnon–parametric formnormal to the planeparametric formperpendicularscalar triple productshortest distanceskew linesvector triple product between the two skew linesis the length of the line segment perpendicular to both the skew lines.

A straight will lie on a plane if every point on the line, lie in the plane and the normal to the plane is  Cartesian equationcoplanarnon–parametric formnormal to the planeparametric formperpendicularscalar triple productshortest distanceskew linesvector triple product to the line