Vector Subtraction

QuestionsVector Subtraction
mrtester asked 3 years ago

Hi,
Is there an easy way to remember the order of the vectors when doing vector subtraction? I struggle to remember from which tip you should go etc.
Thanks in advance!
/mrtester

1 Answers
jacobstrom Staff answered 3 years ago

Hi!
Since addition is a bit easier than subtraction, my way of remembering this is based on addition. To summarize your question, assume you have the following situation:

Now is $\vc{c}$ equal to $\vc{a}-\vc{b}$ or to $\vc{b}-\vc{a}$? I can never remember. So I use addition:
Clearly, if we go from the lower left point and follow $\vc{a}$ and then $\vc{c}$ we arrive at $\vc{b}$. Hence,
\begin{equation}
\vc{a} + \vc{c} = \vc{b}.
\end{equation} Now if we move $\vc{a}$ to the other side we get
\begin{equation}
\vc{c} = \vc{b} – \vc{a},
\end{equation} and we have the answer without having to memorize tip points and tail points.
Hope this works for you too!
Best Regards,
-Jacob

mrtester replied 3 years ago

Thanks for the answer, I have closed the question.