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

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.

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 $$\overrightarrow{ZX}$$.

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