3.7 Vectors

Use standard notations for vectors: column vectors with components x, y or x, y, z; xi + yj; xi + yj + zk; AB with an arrow over it; and a bold letter such as a.

Taught in: Vector notation — the language of vectors · 4 questions

Carry out addition and subtraction of vectors and multiplication of a vector by a scalar, and interpret these operations in geometrical terms.

For example, 'OABC is a parallelogram' is equivalent to the vector OB being equal to the vector OA plus the vector OC. The general form of the ratio theorem is not included, but candidates are expected to understand that the midpoint of AB has position vector ½(OA + OB), where OA and OB are vectors.

Taught in: Adding vectors and multiplying by scalars · 5 questions

Calculate the magnitude of a vector, and use unit vectors, displacement vectors and position vectors.

In 2 or 3 dimensions.

Taught in: Magnitude and unit vectors · 7 questions

Understand the significance of all the symbols used when the equation of a straight line is written in the form r = a + tb, and find the equation of a line given sufficient information.

For example, finding the equation of a line given the position vector of a point on it and a direction vector, or given the position vectors of two points on it.

Taught in: The vector equation of a line: r = a + tb · 3 questions

Determine whether two lines are parallel, intersect or are skew, and find the point of intersection of two lines when it exists.

Calculating the shortest distance between two skew lines is not required, and neither is finding the equation of the common perpendicular to two skew lines.

Taught in: Line relationships — parallel, intersecting, or skew · 4 questions