Vectors
A vector has both a size and a direction. It is written as a column of numbers showing the move across and up.
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Analogy
Like a treasure map instruction: 'go 3 steps east and 2 steps north'.
Example
a + b = (4, 6)2a = (6, 4)b - a = (-2, 2)
In practice
Wind, force and a boat's course across a river are all vectors.
Practice
Flashcards
- Add the vectors (3, 2) and (1, 4).(4, 6).
Questions people ask
How do you add two vectors?
Add the top numbers together and add the bottom numbers together. For (3, 2) + (1, 4), you get (3 + 1, 2 + 4) = (4, 6). It is the same as doing one move after the other. Subtraction works in the same way: take the matching numbers away from each other instead.
What does multiplying a vector by a number do?
It stretches or shrinks the vector, but keeps its direction. Multiply both numbers by the scalar. So 2 x (3, 2) = (6, 4), which is twice as long. A negative number also reverses the direction. Dividing by a number works the same way and shrinks the vector instead.