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

Fluency in arithmetic procedures with 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

Parallel vectors in algebraic vector notation

The sum and difference 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

Vector $$\overrightarrow{AB}$$ is equivalent to __________.

$$\overrightarrow{OY} = 10\mathbf{a} + 9\mathbf{b}$$

$$\overrightarrow{OY} = 40\mathbf{a} + 36\mathbf{b}$$

$$\overrightarrow{OY} = 5\mathbf{a} + 9\mathbf{b}$$

$$\overrightarrow{OY} = 20\mathbf{a} + 9\mathbf{b}$$

Vector $$\overrightarrow{OA} = 20\mathbf{a} + 18\mathbf{b}$$. $$Y$$ is the midpoint of $$\overrightarrow{OA}$$. Find the vector $$\overrightarrow{OY}$$ in terms of $$\mathbf{a}$$ and $$\mathbf{b}$$

$$\overrightarrow{OB} = 10\mathbf{a} + 9\mathbf{b}$$

$$\overrightarrow{OB} = 40\mathbf{a} + 36\mathbf{b}$$

$$\overrightarrow{OB} = 5\mathbf{a} + 9\mathbf{b}$$

$$\overrightarrow{OB} = 20\mathbf{a} + 9\mathbf{b}$$

Vector $$\overrightarrow{OA} = 20\mathbf{a} + 18\mathbf{b}$$. $$A$$ is the midpoint of $$\overrightarrow{OB}$$. Find the vector $$\overrightarrow{OB}$$ in terms of $$\mathbf{a}$$ and $$\mathbf{b}$$ 

$$\frac{1}{2}\overrightarrow{BD}=\overrightarrow{BX}$$

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

$$\frac{1}{2}\overrightarrow{BD}=0.5\bigg({2\choose3}+{6\choose-1}\bigg)$$

$$\frac{1}{2}\overrightarrow{BD}= 2\bigg({2 \choose 3}+{6 \choose -1}\bigg)$$

$$X$$ is the midpoint of the vector $$\overrightarrow{BD}$$. Which of the following statements are true?

$$\overrightarrow{PX}= 14\mathbf{a}-16\mathbf{b}$$ 

$$\overrightarrow{PX}= 7\mathbf{a}-8\mathbf{b}$$ 

$$\overrightarrow{PX}= 7\mathbf{a}+8\mathbf{b}$$

$$\overrightarrow{PX}= 3.5\mathbf{a}-4\mathbf{b}$$ 

$$X$$ is the midpoint of the vector $$\overrightarrow{PQ}$$. Which of the following is vector $$\overrightarrow{PX}$$?

$$\overrightarrow{OX}= 1.5\mathbf{a}+0.5\mathbf{b}$$ 

$$\overrightarrow{OX}= 3\mathbf{a}-\mathbf{b}$$ 

$$\overrightarrow{OX}= 1.5\mathbf{a}-0.5\mathbf{b}$$ 

$$\overrightarrow{OX}= 2.5\mathbf{a}-\mathbf{b}$$ 

$$\overrightarrow{OX}= 2.5\mathbf{a}+\mathbf{b}$$ 

The point $$X$$ is the midpoint of the vector $$\overrightarrow{OB}$$. Identify $$\overrightarrow{OX}$$.

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

Which of these vectors can be represented as $${-2 \choose -2}$$ in column form?

Which of these vectors can be represented as $${2\choose 3}$$ in column form?

Which of the following is equivalent to the resultant vector $${16 \choose -13} $$?

You are given that $$\overrightarrow{OB}= \mathbf{a}$$ and $$\overrightarrow{OA}=\mathbf{b}$$. Which of the following is the vector $$\overrightarrow{AB}$$?

Which vector can be written in the form  $$3\mathbf{a} -\mathbf{b} + 3\mathbf{d}$$?

Fluency in arithmetic procedures with algebraic vector notation

Lesson outcome