Graphical Subtraction of Parallel Vectors: Example 1

Let’s subtract these vectors graphically to get D = A - B. Can we do this if the vectors are parallel?

Yes.

How?

Consider D = A – B.  We can rewrite this as a vector sum involving –B.

Do that.

We get D = A + (–B), or D requires vector addition of the negative of B.

How is the magnitude of (-B), related to the magnitude of B?

They are the same.

How is the direction of (-B), related to the direction of B?

They are in opposite directions.

How are the units of (-B) related to the units of B?

They are the same.

Draw vectors A and (-B) on paper.  Then click “Next” to check your diagram.

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What do we do next to add A and (-B)?

We move (-B) into head-to-tail position with A.

Draw A and (-B) in “head-to-tail” position on paper, and then click “Next” to check your work.

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Describe the drawing of the vector sum D = A + (-B) in terms of the tail of A and the head of (-B).

The vector sum A + (-B) is drawn from the tail of A to the head of (-B)

Show D = A + (-B) in a paper diagram, and then click “Next” to check your diagram.

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Let's review how we got this diagram: 
We constructed (-B) by reversing B. 
We added (-B) to A by moving (-B) so that its tail was located at the head of A.
We then drew D from the tail of A to the head of (-B).

Describe how the units of A, (-B), and D are related.

A and (-B) had to have the same units in order for us to be able to add them.  D has the same units as A and (-B).

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