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Maths · Vectors, Constructions and Loci

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Maths · AQA Paper 2

Vectors, Constructions and Loci

Column Vectors and Vector Arithmetic

Writing vectors as columns, adding, subtracting and multiplying them, and spotting parallel vectors.

  • Vector A quantity with a size and a direction.
  • Column vector A vector written with the horizontal move above the vertical move.
  • Scalar An ordinary number, such as 3, used to multiply a vector.
A vector a from A to B on a grid, which moves 3 to the right and 2 up, with a second equal vector drawn elsewhere.

Vector Geometry and Proof

Finding vectors by routes around a diagram, dividing lines in a ratio, and proving lines parallel or points collinear.

  • Vector proof A proof that uses vectors to show a geometric fact.
  • Route A path from one point to another made from known vectors.
  • Collinear Lying on the same straight line.
Triangle OAB with OA equal to a and OB equal to b, the midpoint M of AB, and a point P two thirds of the way along OB.

Ruler-and-Compass Constructions

Constructing perpendicular bisectors, angle bisectors, perpendiculars and triangles with ruler and compasses.

  • Construction An accurate drawing made with a ruler and compasses.
  • Bisect To cut into two equal parts.
  • Perpendicular bisector A line that bisects another line at right angles.
The construction of the perpendicular bisector of the line AB with two pairs of arcs and a straight line through the crossing points.

Loci

Drawing and shading regions defined by distances from points and lines, using bisectors and circles.

  • Locus The set of all points that follow a given rule.
  • Loci More than one locus.
  • Equidistant The same distance from two or more things.
A circle of radius 2 cm around the point A, and the perpendicular bisector of the line joining A and B.

Bearings, Scale Drawings, Plans and Elevations

Three-figure bearings and back bearings, map scales, and the plan and elevations of simple solids.

  • Bearing A direction given as an angle measured clockwise from north.
  • Three-figure bearing A bearing written with three figures, such as 045.
  • North line A line pointing north, from which a bearing is measured.
The bearing of B from A is 065 degrees, and the bearing of A from B is 245 degrees, shown with north lines at both points.