menu

arrow_back What is the form of vector and parametric equations of lines in $R^{2}$ and $R^{3}$

by Platinum
(106,962 points)
in Mathematics
7 views
What is the form of vector and parametric equations of lines in $R^{2}$ and $R^{3}$

1 Answer

Best answer
0 like 0 dislike
 
Best answer
The variable $t$ (called a parameter) varies from $-\infty$ to $\infty$, the point $\mathbf{x}$ traces out the line $L$.

Accordingly, we have the following result. Let $L$ be the line in $R^{2}$ or $R^{3}$ that contains the point $\mathbf{x}_{0}$ and is parallel to the nonzero vector $\mathbf{v}$.

Then the equation of the line through $\mathbf{x}_{0}$ that is parallel to $\mathbf{v}$ is $$ \mathbf{x}=\mathbf{x}_{0}+t \mathbf{v} $$ If $\mathbf{x}_{0}=\mathbf{0}$, then the line passes through the origin and the equation has the form $$ \mathbf{x}=t \mathbf{v} $$
by Platinum
(106,962 points)

Related questions


Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Define a vector
1 answer 11 views
Define a vectorDefine a vector ...
by MathsGee Platinum
(106,962 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
You may choose the same option for matching more than once. Read through the following proof and spot an error or not in the lines $L 1$ to $L 5$.

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
You may choose the same option for matching more than once. Read through the following proof and match the lines with the reasons given below.
0 answers 9 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Is it possible to have $\operatorname{proj}_{\mathrm{a}} \mathbf{u}=\operatorname{proj}_{\mathbf{u}} \mathbf{a} ?$ Explain.
0 answers 7 views
close

Join the MathsGee Homework Help Q&A club where you get study support for success from our verified experts. Subscribe for only R100 per month or R960 per year.


On the MathsGee Homework Help Q&A learning community, you can:


  1. Ask questions
  2. Answer questions
  3. Comment on Answers
  4. Vote on Questions and Answers
  5. Donate to your favourite users
  6. Create/Take Live Video Lessons

Posting on the MathsGee Homework Help Q&A learning community


  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

MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

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

Management Leadership | MathsGee ZOOM | eBook | H5P