;
Learning starts with a question. Asking is a signal for knowledge request!
First time here? Checkout the FAQs!
x

*Math Image Search only works best with SINGLE, zoomed in, well cropped images of math. No selfies and diagrams please :)

0 like 0 dislike
478 views
How do I write vectors whose initial point is not at the origin?
in Mathematics by Platinum (101k points) | 478 views

1 Answer

0 like 0 dislike
Best answer

It is sometimes necessary to consider vectors whose initial points are not at the origin. If $\overrightarrow{P_{1} P_{2}}$ denotes the vector with initial point $P_{1}\left(x_{1}, y_{1}\right)$ and terminal point $P_{2}\left(x_{2}, y_{2}\right)$, then the components of this vector are given by the formula
$$
\overrightarrow{P_{1} P_{2}}=\left(x_{2}-x_{1}, y_{2}-y_{1}\right)
$$
That is, the components of $\overrightarrow{P_{1} P_{2}}$ are obtained by subtracting the coordinates of the initial point from the coordinates of the terminal point. For example, in Figure 3.1.12 the vector $\overrightarrow{P_{1} P_{2}}$ is the difference of vectors $\overrightarrow{O P_{2}}$ and $\overrightarrow{O P_{1}}$, so
$$
\overrightarrow{P_{1} P_{2}}=\overrightarrow{O P_{2}}-\overrightarrow{O P_{1}}=\left(x_{2}, y_{2}\right)-\left(x_{1}, y_{1}\right)=\left(x_{2}-x_{1}, y_{2}-y_{1}\right)
$$
As you might expect, the components of a vector in 3 -space that has initial point $P_{1}\left(x_{1}, y_{1}, z_{1}\right)$ and terminal point $P_{2}\left(x_{2}, y_{2}, z_{2}\right)$ are given by
$$
\overrightarrow{P_{1} P_{2}}=\left(x_{2}-x_{1}, y_{2}-y_{1}, z_{2}-z_{1}\right)
$$

 

triangle2

 

by Platinum (101k points)

Related questions

0 like 0 dislike
0 answers
0 like 0 dislike
1 answer
0 like 0 dislike
1 answer

Join MathsGee Q&A, where you get instant answers to your questions from our AI, AstraNova and verified by human experts. We use a combination of generative AI and human experts to provide you the best solutions to your problems.

On the MathsGee Q&A, you can:

1. Get instant answer to your questions

2. Convert image to latex

3. AI-generated answers and insights

4. Get expert-verified answers

5. Vote on questions and answers

6. Tip your favorite community members

7. Join expert live video sessions (Paid/Free)

8. Earn points by participating

9. Take a course

10. Enjoy our interactive learning resources


Posting on the MathsGee Q&A

1. Remember the human

2. Act like you would in real life

3. Find original source of content

4. Check for duplicates before publishing

5. Read the community guidelines


MathsGee Q&A Rules

1. Answers to questions will be posted immediately after moderation

2. Questions will be queued for posting immediately after moderation

3. Depending on the number of messages we receive, you could wait up to 24 hours for your message to appear. But be patient as posts will appear after passing our moderation.


MathsGee Q&A


Acalytica


Social Proof


Web Analytics


Courses