Vectors, scalar and vector products (HL)

Learning objectives

Represent vectors as directed line segments, in column form and in terms of the base vectors i, j and k, and distinguish position vectors from displacement vectors

Add and subtract vectors, multiply a vector by a scalar, find the magnitude of a vector and the unit vector in its direction, and identify parallel vectors, using both algebraic and geometric approaches

Use position vectors to find the displacement vector between two points and to prove geometrical properties such as parallelism, collinearity and midpoints

Calculate the scalar product of two vectors, use it to find the angle between them, and test whether vectors are perpendicular or parallel

Calculate the vector product of two vectors, use its properties, and interpret |v × w| as the area of the parallelogram spanned by v and w