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

The sum and difference with algebraic vector notation

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

Match each vector to the correct column vector.

Match each combination of vectors to the correct resultant.

Given $$\mathbf{a}={1\choose 3}$$ and $$\mathbf{b}={2\choose -3}$$, write the resultant vector in terms of $$\mathbf{a}$$ and $$\mathbf{b}$$.

Find the vector $$\overrightarrow{PQ}$$ in terms of $$\mathbf{a}$$ and $$\mathbf{b}$$.

$$3\mathbf{a} -\mathbf{b} + 3\mathbf{d}$$ 

$$\mathbf{a} -4\mathbf{b} + 3\mathbf{d}$$ 

$$\mathbf{a} -3\mathbf{b} + 3\mathbf{d}$$ 

$$-\mathbf{a}-4\mathbf{b} - 2\mathbf{d}$$ 

Match each vector to the correct vector pathway.

A vector starting from $$A$$ and ending at $$B$$

A line segment with points $$A$$ and $$B$$ at each end

A vector starting from $$B$$ and ending at $$A$$

A point with $$x$$-coordinate of $$a$$ and $$y$$-coordinate of $$b$$

A point with $$x$$-coordinate of $$b$$ and $$y$$-coordinate of $$a$$

Match the correct statement with the correct notation.

Which of the following represents this vector?

$$\overrightarrow{DF}=\overrightarrow{DC}+\overrightarrow{CF}$$

$$\overrightarrow{AC}=\overrightarrow{AB}-\overrightarrow{BC} $$

$$\overrightarrow{EC}=-\overrightarrow{DE}-\overrightarrow{CD} $$

$$\overrightarrow{DC}=-\overrightarrow{CD}$$

$$\overrightarrow{BD}=\overrightarrow{CB}+\overrightarrow{CD} $$

Which of the following vector pathways are correct?

$${13 \choose -2} + {12 \choose 7} = {25 \choose x} $$

$${12 \choose x} + {-7 \choose -7} = {5 \choose -14} $$

$${3\choose 4} + {x \choose -4} = {11 \choose 0} $$

Match each $$x$$ value to the correct vector statement.

This lesson will be removed by end of Summer Term 2025.

The sum and difference with algebraic vector notation

Lesson outcome

This lesson will be removed by end of Summer Term 2025.