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

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

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

Starter Quiz