What you’ll learn6 learning objectivesChoose one objective for a focused lesson, or study the complete topic.3.7.1Standard notations for vectors• use standard notations for vectors, i.e. x yfp, xi + yj, x y z fp, xi + yj + zk, AB, aSyllabus objective3.7.2Vector operations• carry out addition and subtraction of vectors and multiplication of a vector by a scalar, and interpret these operations in geometrical terms e.g. 'OABC is a parallelogram' is equivalent to OB OA OC= +. The general form of the ratio theorem is not included, but understanding that the midpoint of AB has position vector OA OB2 1 +_ i is expected.Syllabus objective3.7.3Position vectors• calculate the magnitude of a vector, and use unit vectors, displacement vectors and position vectors In 2 or 3 dimensions.Syllabus objective3.7.4Straight lines• understand the significance of all the symbols used when the equation of a straight line is expressed in the form r = a + tb, and find the equation of a line, given sufficient information e.g. finding the equation of a line given the position vector of a point on the line and a direction vector, or the position vectors of two points on the line.Syllabus objective3.7.5Whether two lines are parallel• determine whether two lines are parallel, intersect or are skew, and find the point of intersection of two lines when it exists Calculation of the shortest distance between two skew lines is not required. Finding the equation of the common perpendicular to two skew lines is also not required.Syllabus objective3.7.6Scalar product• use formulae to calculate the scalar product of two vectors, and use scalar products in problems involving lines and points. e.g. finding the angle between two lines, and finding the foot of the perpendicular from a point to a line; questions may involve 3D objects such as cuboids, tetrahedra (pyramids), etc. Knowledge of the vector product is not required.Syllabus objective