How To Find The Vector Equation of a Line and Symmetric & Parametric Equations
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- เผยแพร่เมื่อ 6 ก.ย. 2024
- This Calculus 3 video tutorial explains how to find the vector equation of a line as well as the parametric equations and symmetric equations of that line in a 3D coordinate system.
3D Coordinate System: • Plotting Points In a T...
3D Distance Formula:
• How To Find The Distan...
Equation of a 3D Sphere:
• How To Find The Equati...
Calculus 3 - Intro to Vectors:
• Calculus 3 - Intro To ...
Calculus 3 - The Dot Product:
• Calculus 3 - The Dot P...
_______________________________
Angle Between Two Vectors:
• Finding The Angle Betw...
Parallel & Orthogonal Vectors:
• Are The Two Vectors Pa...
Direction Cosines and Vectors:
• Calculus 3 - Direction...
Calculus 3 - Vector Projections:
• Calculus 3 - Vector Pr...
Cross Product of 2 Vectors:
• Cross Product of Two V...
_______________________________
Area - Vector Cross Product:
• Area of a Parallelogra...
Triple Scalar Product:
• Volume of a Parallelep...
Vector Equations of Lines:
• How To Find The Vector...
The Equation of a Plane:
• How To Find The Equati...
Planar Equation - 3 Points:
• How To Find The Equati...
________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
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Vectors - Free Formula Sheet:
bit.ly/3WYIGOv
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Vectors - Free Formula Sheet: bit.ly/3WYIGOv
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Vector Equation of the Line 4:06. Parametric Equation 4:07. Symmetric Equations 5:38.
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Ok
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Personal Notes:
1. Vector Equation 2. Parametric Equation 3. Symmetric Equation of/for a line
1:30 Also Check Dr ___ video on this topic
4:04
4:10
5:15
5:33 Part C
7:00L
Greetings, sir!
I would like to ask something I found unclear: When we have two given points, and we found the vector e.g. AB, how do we decide which point do we plug into the line equation, point A or B? Or it doesn't matter?
Thank you!
doesn't matter
you will plot the starting point because Point A is the Po point or you can say ro vector and AB is the same as the vector g or v(parallel to g) which is difference between the point B to A
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7:48 why he didnt take point b instead of point a ??
You may take any point no problem for that.
@@RakibSWN but you will get different solutions
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the position vectors of the points A and B are (1.4.6) and (3.5.7) .find the vector equation of the line AB and find the points where the line intersects the coordinate planes??
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Damn good this video is! Bro, you've just made the topic line segment sound like 'water'!
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What is i use vector BA as my vector and i use the point B as my P nought .......will we arrive at the same answer
Thanks
thanks
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This was very helpful, thank you!
so you're telling me
I just spent 4 hours in my lecture class not understanding a thing of what my teacher was saying. and it was literally this easy lol.
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How's r the equation of the line. Its not parallel to g or v?
Thanks a lot
Good job
having found the vector equation of the line how would you then find another point, the end point, given only one of the 3 coordinates?
The question im facing:
Point B = [40,0,-20]
Point C = [a,b,0]
Direction of the vector = 3i + 4j + k
"Write down a vector equation of the line BC. Hence find a and b"
Any help greatly appreciated.
Here are my assumptions about this questions
Assume that we have point A(0,0,0)
so we can take a vector from AB =
BC= =
AC = AB+BC=point C=
from what we know, Direction of the vector = 3i + 4j + k or
this vector suppose to parallel to vector BC
then we can write BC= t ,where t = scalar
=
from the equation above we get new equation below
t=20,so a=100 and b=80
CMIIW~
so sorry if i'm wrong
@@kabotero9408 I have submitted my answer now, but that's pretty much what I put so thank you and lets hope you're right
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The question at the top we can't see well too small fount size and sound too low
what if it's perpendicular for number 1????
thank you. again.
Thank you Sir
what if it's perpendicular? please answer
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What if you are given a point and told that it is parallel to one of the axis?
Not sure, but wont the only difference in cords be in the axis that is parallel and the rest 2 be constant.
If you're given a line with a point (1,2,3) and its parallel to x, that means (2,3),the y and z will be constant, and only the x cord will be different.
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Thanks!
and why do we want to find r? don't we want to find L?
why point A? can it be either? 7:49
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SO WHAT ABOUT IF WE APPLY THE FORMULA OF EQUATION OF LINE WITH TWO POINTS? r= (1-t)r1+tr2, I got the same applying this formula
Why g=tv? i´m can´t understand english very well.
Because we want a new vector g to be parallel with V. We let g to be t times far away from v, only the distance changes, direction doesn't change. Do you understand my explanation?
@@cutieboo233 Wow, I was thinking that this was another vector, or a constant, explained it very well. I basically didn't understand that t was to find a vector with the same direction and "sense", but a Module t times V. Thanks...
@@mfq8334 You are welcome! Now you got it, goodluck for you!! ^^
MFQ ! Not module t the vector can have opposite direction although they are parallel
"Let's find the perm...excuse me, the parametric equation"🙃
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