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Physics Lesson 2.2.4 - The Parallelogram (tail-to-tail) Rule
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Welcome to our Physics lesson on The Parallelogram (tail-to-tail) Rule, this is the fourth lesson of our suite of physics lessons covering the topic of Addition and Subtraction of Vectors, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
The Parallelogram (tail-to-tail) Rule
According to this rule, if we put the two vectors a⃗ and b⃗ at the same starting point (tail), the resultant (sum) vector will be the diagonal of the parallelogram formed by these two vectors (we draw other two sides that are in parallel to the given vectors in order to form the parallelogram). Look at the figure 8:
Figure 8. The Parallelogram Rule for the addition of vectors
As for the difference, we revert again the second vector b⃗ to obtain the vector ( -b⃗ ) and apply again the parallelogram rule for the addition of vectors. Look at the figure below.
Figure 9. The Parallelogram Rule for the subtraction of vectors
We can deduce two conclusions from all the above figures:
The vector sum c⃗ = a⃗ + b⃗ is the same in both methods (figure 6 and 8), and the vector difference d⃗ = a⃗-b⃗ is the same in both methods as well (figure 7 and 9); whatever method you choose, it gives the same result.
If the vector sum gives the diagonal of the parallelogram formed by the two vectors and their parallel extensions (figure 8), the vector difference gives the other diagonal of the same parallelogram (figure 9).
You have reach the end of Physics lesson 2.2.4 The Parallelogram (tail-to-tail) Rule. There are 5 lessons in this physics tutorial covering Addition and Subtraction of Vectors, you can access all the lessons from this tutorial below.
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- Continuing learning vectors and scalars - read our next physics tutorial: Multiplication of a Vector by a Scalar
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