Intersections of Lines & Planes How do I tell if a line is parallel to a plane? A line is parallel to a plane if its direction vector is perpendicular to the plane’s normal vector If you know t...
Equation of a Plane in Vector Form How do I find the vector equation of a plane? A plane is a flat surface which is two-dimensional Imagine a flat piece of paper that continues on forever in both d...
Shortest Distance between a Point & a Line How do I find the shortest distance from a point to a line? The shortest distance from any point to a line will always be the perpendicular distance G...
Scalar Product The scalar product is an important link between the algebra of vectors and the trigonometry of vectors. We shall see that the scalar product is somewhat comparable to the operation o...
Coincident & Parallel Lines How do I tell if two lines are parallel? Two lines are parallel if, and only if, their direction vectors are parallel This means the direction vectors will be scalar...
Equation of a Line in Vector Form How do I find the vector equation of a line? You need to know: The position vector of one point on the line A direction vector of the line (or the position vector ...
Integrating using Trigonometric Substitutions The integrals covered in this revision note are based on the standard results and These are given in the formulae booklet How do I know when to use a t...
Differentiating Inverse Trig Functions What are the inverse trigonometric functions? arcsin, arccos and arctan are functions defined as the inverse functions of sine, cosine and tangent respectivel...
Integrating with Partial Fractions What is meant by partial fractions with quadratic denominators? For linear denominators the denominator of the original fraction can be factorised such that the d...
