Learning objectives
Use column vectors, i, j, k notation, position vectors and displacement vectors such as AB = b − a in two and three dimensions
Add, subtract and scale vectors and interpret the results geometrically, for example to find the fourth vertex of a parallelogram, a midpoint ½(a + b) or to show that three points are collinear
Calculate the magnitude of a vector and find a unit vector in a given direction
Write the equation of a line as r = a + tb from given information, and decide whether two lines are parallel, intersect (finding the point of intersection) or are skew
Use the scalar product a·b = |a||b| cos θ to find the angle between two lines, show that vectors are perpendicular and find the foot of the perpendicular from a point to a line and hence the shortest distance
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