Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.

Parallel vectors in algebraic vector notation

Maths

Checking and securing understanding of translations

Column vectors

Parallel vectors

Addition with vectors

Subtraction with vectors

Multiplication with vectors

Fluency in arithmetic procedures with vectors

Algebraic vector notation

The sum and difference with algebraic vector notation

Fluency in arithmetic procedures with algebraic vector notation

Calculating the magnitude of a vector

Dividing vectors into ratios

Geometric proofs with vectors

Advanced problem solving with vectors

In the prior unit, pupils described a translation using column vector notation. Pupils' understanding of vectors is further developed in this unit, with pupils exploring column vector notation and arithmetic procedures.

In this unit, pupil understanding of vectors is deepened with pupils exploring column vector notation and arithmetic procedures.

Vectors

Select the correct statements for parallel vectors. Parallel vectors __________.

Which of these vectors are parallel to $${4 \choose -3}$$?

Which of these vectors are parallel to $$3\mathbf{a}+5\mathbf{b}$$?

Match each vector to a vector that is parallel to it.

$$\frac{1}{2}\overrightarrow{AB}=\overrightarrow{MN}$$

$$2\overrightarrow{MN}=\overrightarrow{AB}$$

$$\frac{1}{3}\overrightarrow{AB}=\overrightarrow{MN}$$

$$3\overrightarrow{MN}=\overrightarrow{AB}$$

OACB is a parallelogram. M is the midpoint of OA and N is the midpoint of OB. $$\overrightarrow{OM}=10\mathbf{a}$$ and $$\overrightarrow{ON}=10\mathbf{b}$$. Select the correct scalar multipliers.

$$\overrightarrow{XY} = \overrightarrow{WZ}$$

$$\overrightarrow{YC} = \overrightarrow{ZD}$$

$$\overrightarrow{AX} = \overrightarrow{AW}$$

$$\overrightarrow{XW} = \overrightarrow{YZ}$$

ABCD is a kite. AX:XB = 1:1, BY:YC = 1:1, DZ:ZC = 1:1 and AW:WD=1:1,  $$\overrightarrow{AW}= 3\mathbf{a}$$, $$\overrightarrow{AX}=3\mathbf{b}$$ and $$\overrightarrow{DZ}=3\mathbf{c}$$.

Parallel vectors must be in the same direction.

Parallel vectors can have different magnitudes.

Parallel vectors may have opposite directions.

All parallel vectors have the same length.

Identify which of these statements are true.

Which of the following vectors are parallel to $${3 \choose 5}$$ ?

Which of the following vectors is parallel to $$\overrightarrow{IA}$$?

Here is a regular hexagon with two labelled vectors. The centre of the hexagon is O. Select the vectors which are parallel to $$\overrightarrow{OX}$$.

Which of the following vectors are parallel to $${2 \choose -3}$$?

Match each column vector to its gradient.

Parallel vectors in algebraic vector notation

Lesson outcome