Topic outline
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Video transcriptThis unit of work is Vectors.
Learners often struggle with the difference between vector and scalar quantities. They can also be confused with Vector notation.
This unit will help to develop learners conceptual understanding of vectors and give them the opportunity to apply their understanding to complex multi-step problems.
For instance learners will understand how vectors can be used to describe the translation of shapes by plotting the translation of each of the individual points.
Extended learners will apply vectors to real life problems including finding the magnitude and direction of a vector. They will also solve problems in Vector Geometry.
This unit of work is just one of several approaches that you could take when teaching this topic and you should aim to adapt the resources to match ability level of your learners as well as your school context.
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Lesson 3 video
Video transcript
As we have already seen a vector has magnitude (size) and direction. When looking at a vector diagram the length of the line shows its magnitude and the arrow represents the direction of the vector.
We're going to start by looking at how you add vectors. We can add two vectors by joining them end on end.
Here you can see two vectors a and b.
To add vector b to vector a you join the tail of vector b to the head of vector a.
The result is a vector that joins the tail of vector a to the head of vector b. This is called the resultant vector a + b.
Think about two non-parallel vectors, a and b. Then a plus b is the translation of a followed by the translation of b.
You should be able to see from the diagram that it doesn't matter which order you add them, you will get the same result.
So a plus b is exactly the same as b plus a.
This tells us that vector addition, like ordinary numerical addition is commutative, in other words the order doesn't matter.
You can add vectors with or without the use of a diagram for example if you want to add two vectors p and q you can add the horizontal components and then the vertical components.
This will give you the vector five-two. Five to the right and two up.
You can always check your results using a diagram.
You can also subtract vectors.
a - b is defined as the translation of a followed by the translation of minus b.
To subtract vector b from vector a you join the tail of vector -b to the head of vector a.
The resultant vector a - b joins the tail of vector a to the head of vector b.
You can see that the resultant vector a minus b can be considered either as a minus b or as minus b plus a.
You can also subtract vectors with or without the use of a diagram by subtracting components.
First subtract the horizontal components and then the vertical components.
In this example the resultant vector is one eight - one to the right and eight up.
This can be pictured on a diagram as follows.
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