Vectors

Prerequisite Knowledge

• Describe translations as 2D vectors
• Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors
• Use vectors to construct geometric arguments and proofs

Success Criteria

• Use vectors in two dimensions
• Calculate the magnitude and direction of a vector;
• Add vectors diagrammatically and perform the algebraic operations of vector addition and multiplication by scalars, and understand their geometrical interpretations;
• Understand and use position vectors; calculate the distance between two points represented by position vectors 
• Use vectors to solve problems in pure mathematics and in context, including forces 

Teaching Points

• Students should sketch diagrams whenever possible as part of their work, reinforcing the algebraic notation.
• By drawing and labelling diagrams, students can better identify a position vector from a direction vector.
• When simplifying or calculating vectors, students should be comfortable using column notation.
• Vector problems .often lead to setting up and solving a pair of simultaneous equations.
• Students need to know how a vector’s magnitude leads to working out a unit vector.
• Vector geometry often leads to problems in non-right-angled triangles, bearings and forces. Students need plenty of practise with these types of problems.
• The resultant vector is the sum of two or more vectors.
• Speed in the magnitude of a velocity vector
• Distance is the magnitude of a displacement vector.

Misconceptions

• Some students lose marks by writing the magnitude of a vector as a negative.
• When writing vectors in i and j notation, some students incorrectly think of it as a coordinate pair and write 3i – 2j as (3i, -2j).
• Some students get confused knowing when a vector gives a direction or a position.