boardworks ltd 2013 1 of 9 s7 vectors maths age 14-16
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© Boardworks Ltd of 9 Representing vectors A B To go from the point A to the point B we must move 6 units to the right and 3 units up. We can represent this movement using a column vector. AB= 6 3 This is the horizontal component. It tells us the number of units in the x -direction. This is the vertical component. It tells us the number of units in the y -direction. 6 3TRANSCRIPT
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S7 Vectors
Maths Age 14-16
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Representing vectors
A vector can be represented using a line segment with an arrow on it.
For example,
A
B
The magnitude of the vector is given by the length of the line.
The direction of the vector is given by the arrow on the line.
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Representing vectors
A
B
To go from the point A to the point B we must move 6 units to the right and 3 units up.
We can represent this movement using a column vector.
AB = 63
This is the horizontal component. It tells us the number of units in the x-direction.
This is the vertical component. It tells us the number of units in the y-direction.
6
3
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Representing vectors
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The negative of a vector
a
A
B–a
A
B
If this is the vector a, this is the vector –a.
The negative of a vector is the same length and has the same slope, but goes in the opposite direction.
In general,
if a = xy then –a = –x
–y
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The negative of a vector
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Adding vectors
When two or more vectors are added together the result is called the resultant vector.
In general, if a = ab and b = c
d
We can add two column vectors by adding the horizontal components together and adding the vertical components together.
a + b = a + cb + d
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Adding and subtracting vectors
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Finding the magnitude of a vector