Consider a straight line passing through the points (0,2,-2) and (2,3,-1) a.) Fi

Question

Consider a straight line passing through the points (0,2,-2) and (2,3,-1)

a.) Find an equation of the line.

b.) Find the coordinates of the point P where the line meets the x-y plane.

c.) Find the coordinates of the point Q where the line meets the x-z plane.

For part (a) I applied the equation r(t)=r+tv and ended up with <2t,2+t,-2+t> and this is correct because if t=0 then I end up with the first set of coordinates and if t=1 then I get the second set of coordinates. My question is more towards (b) and (c). If I wanted to find the coordinates of where it meets the designated plane do I just drop the term that's not included? For example, in part (b) do I just drop the -2+t and set the 2t equal to 2+t? Please help me.

Explanation / Answer

B) xy plane implies z=0, therefore -2+t=0 or t =2

Hence co ordinates are(4,4,0)

C) xz plane implies y=0, therefore 2+t=0 or t =-2

Hence co ordinates are(-4,0,-4)

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