Find the Intersection Point of a Line and Plane: Step by Step Guide

  • Thread starter Thread starter lakitu
  • Start date Start date
  • Tags Tags
    Coordinate
AI Thread Summary
To find the intersection point of the given line and plane, start by substituting the line's equations x = -4t + 4, y = -4t + 6, and z = 5t + 5 into the plane equation 4x - 2y + 6z = 78. This substitution will yield a linear equation in terms of t. Solve this equation for t, then use the value of t to calculate the corresponding x, y, and z coordinates from the line's equations. This process will provide the intersection point of the line and the plane. Following these steps will ensure the solution is accurate.
lakitu
Messages
27
Reaction score
0
coordinate help please :)

Hi i just got my home work but don't know where to start. Any help on this just to get me started would be great:) I want to make sure I am doing it right

Thank you


Work out the coordinates where this line meets this plane.

Line x = -4 t + 4, y = -4 t + 6, z = 5 t + 5 and plane 4 x - 2 y + 6 z = 78.
 
Physics news on Phys.org
Plug your expressions for x,y,z into the plane definition. You now have an equation (linear) for t. Solve for t and plug it into your x,y,z definitions for the line.
 
hey thank you for replying i will give that a go :)
 

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
Find integer points on this equation
Replies
8
Views
1K
Find the coordinates of a point C from the given line, point and circle
Replies
8
Views
2K
Equal intercept on the three axes
Replies
6
Views
2K
Condition for coplanarity of two lines
Replies
14
Views
3K
B: Calculate the distance between two points without using a coordinate system
Replies
20
Views
3K
Intersection of two line segments from uniform distribution
Replies
17
Views
2K
Find the scalar, vector, and parametric equations of a plane
Replies
8
Views
3K
Find the equation of the plane given point and line (3D)
Replies
2
Views
3K
Find Co-ordinates of Point C in Problem Involving Straight Line Equations
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top