Question

Points P(-2,4,3) and Q(-3,0,3) lie on line L. Does a point exist where line L intersects the XZ-Plane? If it does what point.

Answer 1

So we have the vector PQ = <-1,-4,0>

Answer 2

And a point is on the xz plane if it has 0 as a z coordinate like so: (x, y, 0)

Answer 3

P(-2,4,3) and Q(-3,0,3)
+2-4-3 +2-4-3
----------------------
0 0 0 <-1,-4, 0>

we need any scalar of this vector soo: <-t,-4t, 0>

and lets apply it to one of the points given

Answer 4

x=-2-t
y= 4-4t
z= 3

is our line

Answer 5

line equation : (-2,4,3) + (-1,-4,0)t
now we need to find t such that (-2-t,4-4t,3)
4-4t = 0 (XZ PLANE)
so t =1
the point is
(-2-1,0,3) -> (-3,0,3)

Answer 6

in order to cut thru the xz plane; y=0

Answer 7

y = 0 what t = 1

x=-2-1 = -3
y= 4-4(1)= 0
z= 3 = 3

Answer 8

Thanks guys

Answer 9

I am struggling with this stuff, its mad complicated, you guys have any tips?

Answer 10

*or girls

Answer 11

.... i have tips, no girls tho that i can give you

Answer 12

is it high school ? (im wondering .. where i live we dont study this in high school)

Answer 13

Nope, community college.

Answer 14

the biggest thing is to draw a picture so that you can see it