Lagrange21 said:Homework Statement
Show that these lines intersect and what is the intersection point?
x=1+t
y=2t
z=1+3t
and
x=3s
y=2s
z=2+s
Homework Equations
The Attempt at a Solution
I don't know how to start, some help please.
3s= 1 +tRay Vickson said:You want x,y and z on the first line to equal x,y and z on the second line. What does that tell you?
RGV
Plug the above value for s & t into the following equations for your two lines.Lagrange21 said:3s= 1 +t
2s=2t
2+s=1+3t
s = t = 1/2
how can I show that the lines intersect?
Lagrange21 said:Homework Statement
Show that these lines intersect and what is the intersection point?
x=1+t
y=2t
z=1+3t
and
x=3s
y=2s
z=2+s
The intersection point of two lines is the point where the two lines meet or cross each other. It is the solution to the equations of the two lines and represents the coordinates of the point where the lines intersect.
To find the intersection point of two lines using equations, you need to solve the equations simultaneously. This can be done by setting the two equations equal to each other and then solving for the variables. The resulting values will be the coordinates of the intersection point.
No, two lines can only intersect at one point. This is because two lines that intersect at more than one point would be considered the same line.
If the two lines are parallel, they will never intersect and there will be no solution for the equations. This means that there is no intersection point for the two lines.
No, two lines that are perpendicular to each other will always intersect at one point. This is because perpendicular lines have opposite reciprocal slopes, which means they will eventually cross each other at a 90-degree angle.