- Year 11
Multiplication with vectors
I can multiply with vectors.
Lesson details
Key learning points
- Vectors can be multiplied by a scalar.
- Vectors cannot be multiplied by each other.
- Multiplication by a scalar can be done when the vectors are in column form.
- Multiplication by a scalar can be done when the vectors are drawn.
Keywords
Scalar - A scalar is a quantity that has magnitude but not direction.
Displacement - Displacement is the distance from the starting point when measured in a straight line.
Common misconception
A reflection of a vector in the x or y axis is not the reverse of a vector. This is often seen with equilateral triangles and vectors.
When multiplying the vectors by -1 this gives the opposite direction of the vector only. The magnitude remains the same. Investigate with pupils by drawing column vectors and multiply by -1 and compare.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Find the additive inverse of $$ -4 \choose 3$$.
Q2.Match each subtraction to its equivalent addition.
$${-3 \choose 2}-{1\choose 4}$$ - $${-3 \choose 2}+{-1\choose -4}$$
$${-3 \choose 2}-{1\choose -4}$$ - $${-3 \choose 2}+{-1\choose 4}$$
$${-3 \choose 2}-{-1\choose 4}$$ - $${-3 \choose 2}+{1\choose -4}$$
$${-3 \choose 2}-{-1\choose -4}$$ - $${-3 \choose 2}+{1\choose 4}$$
Q3.Match each subtraction to its resultant.
$${-3 \choose 2}-{1\choose 4}$$ - $${-4\choose -2}$$
$${-3 \choose 2}-{1\choose -4}$$ - $${-4 \choose 6}$$
$${-3 \choose 2}-{-1\choose 4}$$ - $${-2 \choose -2}$$
$${-3 \choose 2}-{-1\choose -4}$$ - $${-2 \choose 6}$$
Q4.You are given that $${2\choose3}- {a\choose-3} = {-3\choose6}$$. The value of $$a$$ is .
Q5.Which vector subtraction can be represented by this diagram?
Q6.You are given that $${7\choose3}- {a\choose3} - {-3\choose-2} = {5\choose2}$$. The value of $$a$$ is .
Assessment exit quiz
6 Questions
Q1.A is a quantity that has magnitude but not direction.
Q2.The vector $$k {1 \choose 2}$$ represents the displacement A to B. The value of $$k$$ is .
Q3.The diagram shows the vector a. Which of the following shows −0.25a?
Q4.Match each scalar and vector to the resultant vector.
$$3{8\choose6}$$ - $$24\choose 18$$
$$-6{-4\choose3}$$ - $$24\choose -18$$
$$2{-12\choose-9}$$ - $$-24\choose -18$$
$$-3{8\choose-6}$$ - $$-24\choose 18$$
Q5.You are given that $$3 {5 \choose -4}= {a \choose b}$$ . Find the value of $$a$$ and of $$b$$.
Q6.You are given that $$x {6 \choose y}={24 \choose -36}$$. Find the value of $$x$$ and of $$y$$.
