A vector can be used to describe a translation.

Displacement is the distance from the starting point when measured in a straight line.

A resultant vector is the single vector that produces the same effect as a combination of other vectors.

Advanced problem solving with vectors

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

Parallel vectors in 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

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

A {{}} vector is the single vector that produces the same effect as a combination of other vectors. 

Given $$\mathbf a = {2 \choose 3}$$ and $$\mathbf b = {-1 \choose 2}$$, find $$4\mathbf a - 2 \mathbf b$$

Given that $$ x\choose 8$$ is parallel to $$ 15 \choose 12$$, then $$x =$$ {{}}

$$ a {3\choose -2} + 4{ 3 \choose b} = {3\choose 14}$$. The value of $$b$$ is {{}}

Given that $$a {2\choose 1} + b{ 4 \choose4}= {16 \choose 14}$$, find the value of $$a + b$$. $$a+b=$${{}}.

$$\mathbf a = {2\choose -3}$$ and $$\mathbf b = {-2 \choose y}$$. Given that $$3 \mathbf a - 2 \mathbf b$$ is parallel to $$30 \choose -51$$, the value of $$y$$ is {{ }}.

Three points that lie along the ___________ are said to be collinear.

$$\overrightarrow{AE}=2\overrightarrow{BD}$$

$$\overrightarrow{EA}=2\overrightarrow{BD}$$

$$2\overrightarrow{AE}=\overrightarrow{BD}$$

$$\overrightarrow{AB}\neq k\overrightarrow{ED}$$

$$\overrightarrow{AB}=\overrightarrow{ED}$$

Select the correct statements to show that $$AEDB$$ is a trapezium.

$$\overrightarrow{AF}=\overrightarrow{EB}$$

$$\overrightarrow{AF}=\overrightarrow{BE}$$

$$\overrightarrow{FA}=\overrightarrow{BE}$$

$$\overrightarrow{AB}=\overrightarrow{FE}$$

$$\overrightarrow{AB}=\overrightarrow{EF}$$

Select the correct statements to show that $$ABEF$$ is a parallelogram.

$$ABCD$$ is a kite. The midpoints of each side are shown. $$\overrightarrow{WX} = k(\mathbf a - \mathbf b)$$ where $$k=$${{}}.

$$ABCD$$ is a kite. $$W,X,Y,Z$$ are midpoints of the lines they lie on. Find $$\overrightarrow{WZ}$$.

$$-2 \mathbf c -4 \mathbf b + 2\mathbf a$$

$$ 2\mathbf c + 4\mathbf b - 2\mathbf a$$

$$ABCD$$ is a kite. $$W,X,Y,Z$$ are midpoints of the lines they lie on. Find $$\overrightarrow{ZX}$$.

Advanced problem solving with vectors

Lesson outcome