Uses of the Scalar Product This revision note covers several applications of the scalar product for vectors – namely, how you can use the scalar product to: find the angle between vectors or lines ...
The Scalar ('Dot') 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...
Parallel, Intersecting & Skew Lines In two dimensions, lines are either parallel or they intersect at a single point. If they are parallel, then either they have no points in common, or they sh...
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 ...
Problem Solving using 3D Vectors Problem-solving with 3-D vectors 3-D vector problems can be solved using the same principles as 2-D vector problems (see Problem Solving using Vectors) Vectors can ...
Vectors in 3 Dimensions What is a 3-D vector? Vectors represent a movement of a certain magnitude (size) in a given directionYou should have already come across (2D) vectors at AS (see Basic Vector...
Problem Solving using Vectors Problem-solving with vectors Vectors can be used to prove two lines are parallel (see Vector Addition) They can also be used to show points are collinear (lie on the s...
Position Vectors What is a position vector? Position vectors describe the position of a point in relation to the origin They are different to direction vectors which describe the direction and dist...
Vector Addition Vector addition Adding vectors together lets us describes the movement between two points The single vector this creates is called the resultant vector Subtracting a vector is the s...
