Math & Data Science Q&A - Get answers from our AI that are verified by human experts
First time here? Checkout the FAQs!
x

*Math Image Search only works best with zoomed in and well cropped math screenshots. Check DEMO

MathsGee Android Q&A


0 like 0 dislike
182 views
How is the norm of a vector related to the Theorem of Pythagoras?
in Mathematics by Platinum (164,290 points) | 182 views

1 Answer

0 like 0 dislike
Best answer
We denote the length of a vector $\mathbf{v}$ by the symbol $\|\mathbf{v}\|$, which is read as the norm of $\mathbf{v}$, the length of $\mathbf{v}$, or the magnitude of $\mathbf{v}$ (the term "norm" being a common mathematical synonym for length). It follows from the Theorem of Pythagoras that the norm of a vector $\left(v_{1}, v_{2}\right)$ in $R^{2}$ is $$ \|\mathbf{v}\|=\sqrt{v_{1}^{2}+v_{2}^{2}} $$ Similarly, for a vector $\left(v_{1}, v_{2}, v_{3}\right)$ in $R^{3}$, it follows and two applications of the Theorem of Pythagoras that $$ \|\mathbf{v}\|^{2}=(O R)^{2}+(R P)^{2}=(O Q)^{2}+(Q R)^{2}+(R P)^{2}=v_{1}^{2}+v_{2}^{2}+v_{3}^{2} $$ and hence that $$ \|\mathbf{v}\|=\sqrt{v_{1}^{2}+v_{2}^{2}+v_{3}^{2}} $$
by Platinum (164,290 points)

Related questions

0 like 0 dislike
1 answer
asked Apr 17, 2022 in Mathematics by Gauss Diamond (75,173 points) | 142 views
0 like 0 dislike
1 answer
asked Jan 13, 2022 in Mathematics by MathsGee Platinum (164,290 points) | 203 views
0 like 0 dislike
1 answer
asked Apr 28, 2020 in Mathematics by MathsGee Platinum (164,290 points) | 176 views
0 like 0 dislike
1 answer
asked Sep 22, 2019 in Mathematics by adminTedsf Wooden Status (2,790 points) | 171 views
0 like 0 dislike
1 answer
0 like 0 dislike
0 answers
0 like 0 dislike
1 answer
asked Jul 29, 2022 in Mathematics by Gauss Diamond (75,173 points) | 76 views
0 like 0 dislike
1 answer
asked Jan 26, 2022 in Mathematics by MathsGee Platinum (164,290 points) | 161 views
1 like 0 dislike
1 answer
asked Aug 9, 2021 in Mathematics by Maths Genie SIlver Status (12,174 points) | 521 views
0 like 0 dislike
0 answers
0 like 0 dislike
1 answer
0 like 0 dislike
1 answer
asked Jan 19, 2022 in Mathematics by Gauss Diamond (75,173 points) | 182 views
0 like 0 dislike
1 answer
asked Jan 26, 2022 in Mathematics by MathsGee Platinum (164,290 points) | 175 views
0 like 0 dislike
0 answers

Join MathsGee and get expert-verified answers to your maths and data science questions fast. We use a combination of generative AI and human experts to provide you the best answers to your questions. Ask a question now!


On the MathsGee, you can:


1. Ask and answer questions


2. Get expert-verified answers


3. Vote on questions and answers


4. Tip your favorite community members


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


6. Earn points by participating


7. Start a Fundraiser



Posting on MathsGee


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 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 Android Q&A

MathsGee Android Q&A