Planes Calculation Help: Find Point of Intersection with Coordinate Planes

In summary, we are considering a new line parallel to the given line and passing through the point P(-3, -4, 3). To find the points of intersection with the xy-plane, we need to set z=0 and solve for t in the x and y equations. However, to find the equation of the line parallel to the given one, we need to solve for t first and then use that value to find the x and y coordinates of the point of intersection.
  • #1
Whatupdoc
99
0
Consider the line which passes through the point P(-3, -4, 3), and which is parallel to the line x=1+6t, y=2+4t,z=3+1t

Find the point of intersection of this new line with each of the coordinate planes:

xy-plane:(_,_,_)
yz-plane:(_,_,_)
yz-plane:(_,_,_)

to find xy-plane, I am thinking that i need to set z=0, but I'm not extactly sure how i would solve for the other two points(x & y). can someone help me?
 
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  • #2
When the line intersects with the xy plane, it will have z=0. Here you can solve for t.
 
  • #3
1+6t=2+4t
t=1/2

and when i plug that 1/2 back in for the x and y equation, i get the wrong answer. I'm not understanding what you are trying to tell me.
 
  • #4
Find the equation of the line parallel to the one given that goes through that point first. Then notice that When it intersects the xy plane, the z component of the line will be 0.
 

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