Finding the Vector Eqn of a Line

  • Thread starter Thread starter d=vt+1/2at^2
  • Start date Start date
  • Tags Tags
    Line Vector
AI Thread Summary
To find the vector equation of a line passing through the point P(2, -1, 3) and perpendicular to the plane defined by 3x - 2y - z = 0, the direction vector can be derived from the normal vector of the plane, which is 3i - 2j - k. The equation of the line can then be expressed as Line(x) = P + td, where P is the point and d is the direction vector. The normal vector of the plane serves as the direction vector for the line. This approach effectively provides the necessary components to formulate the vector equation. Understanding the relationship between the plane's normal vector and the line's direction is crucial in solving this problem.
d=vt+1/2at^2
Messages
9
Reaction score
0

Homework Statement



Find the Vector eqn of a line which passes through P(2, -1, 3) and is perpendicular to the plane 3x -2y -z =0.

Homework Equations



Line(x) = P + td where d is a direction vector

The Attempt at a Solution



My main problem here is trying to find the direction vector for the line. I have really no idea how to find that. Any help is greatly appreciated :)
 
Physics news on Phys.org
I think I figured it out...I can use the normal vector of the plane as my direction vector.
 
Yes, that's exactly right. And that, of course, is just 3i- 2j- k.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Is (y + z)x1 = (y1 + z1)x the equation of a straight line in 3D space?
Replies
17
Views
2K
Line of intersection of two planes
Replies
9
Views
3K
Writing vector and parametric equations for a line that....
Replies
5
Views
2K
Vector of shortest distance between two skew lines
Replies
11
Views
3K
Find the scalar, vector, and parametric equations of a plane
Replies
8
Views
3K
Does the line lie in the plane?
Replies
1
Views
2K
Find the equation of the plane parallel to two lines
Replies
6
Views
5K
Angle between a plane and a line
Replies
2
Views
2K
Why does the cross product of two direction vectors....
Replies
2
Views
2K
Writing parallel vector equation
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top