menu

arrow_back What is the mathematical definition of the distance between two vectors in $R^n$?

by Platinum
(119,140 points)
in Mathematics
78 views
What is the mathematical definition of the distance between two vectors in $R^n$?

1 Answer

Best answer
0 like 0 dislike
If $\mathbf{u}=\left(u_{1}, u_{2}, \ldots, u_{n}\right)$ and $\mathbf{v}=\left(v_{1}, v_{2}, \ldots, v_{n}\right)$ are points in $R^{n}$, then we denote the distance between $\mathbf{u}$ and $\mathbf{v}$ by $d(\mathbf{u}, \mathbf{v})$ and define it to be $$ d(\mathbf{u}, \mathbf{v})=\|\mathbf{u}-\mathbf{v}\|=\sqrt{\left(u_{1}-v_{1}\right)^{2}+\left(u_{2}-v_{2}\right)^{2}+\cdots+\left(u_{n}-v_{n}\right)^{2}} $$
by Platinum
(119,140 points)

Related questions


Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the mathematical definition of "Nominal and effective interest rates"?
1 answer 83 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the mathematical definition of "Compound decay or depreciation"?
1 answer 67 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the mathematical definition of "Simple decay or depreciation"?
1 answer 63 views
What is the mathematical definition of "Simple decay or depreciation"?What is the mathematical definition of "Simple decay or depreciation"? ...
by Pieter Gold Status
(31,957 points)
asked in Economics and Finance Jan 11
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}\right)$ and the line $a x+b y+c=0$ in $R^2$?
1 answer 213 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$
1 answer 58 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the distance between the vectors $u=\left(a_{1}, a_{2}, \ldots, a_{n}\right)$ and $v=\left(b_{1}, b_{2}, \ldots, b_{n}\right)$ in $\mathbf{R}^{n}$?

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Prove that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ is
1 answer 222 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
WHat is the definition of a line in $R^n$
1 answer 86 views
WHat is the definition of a line in $R^n$WHat is the definition of a line in $R^n$ ...
by Maths Genie Bronze Status
(5,562 points)
asked in Mathematics Aug 9, 2021
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the definition of subtraction?
1 answer 94 views
What is the definition of subtraction?What is the definition of subtraction? ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Jan 11
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What are the components of mathematical discourse?
1 answer 84 views
What are the components of mathematical discourse?What are the components of mathematical discourse? ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Jan 15
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is mathematical discourse?
1 answer 58 views
What is mathematical discourse?What is mathematical discourse? ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Jan 15
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the definition of an ordered n-tuple?
1 answer 53 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
The angle between vectors $(1,3,-2)$ and $(4,-2,-1)$ is
0 answers 160 views
The angle between vectors $(1,3,-2)$ and $(4,-2,-1)$ isThe angle between vectors $(1,3,-2)$ and $(4,-2,-1)$ is   A) 0 B) $\dfrac{\pi}{3}$ C) $\dfrac{\pi}{2}$ D) $\pi$ E) none of the above ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Jan 13
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
The angle between vectors $(2,6,-4)$ and $(4,-2,-1)$ is
0 answers 150 views
The angle between vectors $(2,6,-4)$ and $(4,-2,-1)$ isThe angle between vectors $(2,6,-4)$ and $(4,-2,-1)$ is   A. 0 B. $\dfrac{\pi}{3}$ C. $\dfrac{\pi}{2}$ D. $\pi$ E. none of the above ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Jan 13
close

Q&A | Subjects | Request Private Tutor | eBook


Join the MathsGee Support Club where you get study and financial support for success from our community. LEARN - CONNECT - EARN


On the MathsGee Support Club, you can:


1. Ask questions


2. Answer questions


3. Vote on Questions and Answers


4. Tip your favourite community member(s)


5. Create Live Video Tutorials (Paid/Free)


6. Join Live Video Tutorials (Paid/Free)


7. Earn points for participating



Posting on the MathsGee Support Club


1. Remember the human


2. Behave like you would in real life


3. Look for the original source of content


4. Search for duplicates before posting


5. Read the community's rules




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 how many posts we receive, you could be waiting up to 24 hours for your post to appear. But, please be patient as posts will appear after they pass our moderation.


Q&A | Subjects | Request Private Tutor | eBook


MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

Q&A | Subjects |Request Private Tutor | eBook