Question

Find the point in which the line that passes through the points (1,0,1) and (4,-2,2) intersects the plane x+y+z=6

Answer 1

Write the equation for the line in parametric form. Then solve for when the ordinates of that form sum to 6.

Answer 2

okay thx dude

Answer 3

would one of the parametric forms be:

x = 1 + 3t
y = -2t
z = 1 + t

?

I also need to study this some time..

Answer 4

yes

Answer 5

so we set the parametric equation = to 6 and solve?

Answer 6

or set t=6?

Answer 7

You set x + y + z = 6 and solve

Answer 8

Which makes sense as it is the only other piece of information you actually have in the problem.

Answer 9

so (5/3, -3, 5)?

Answer 10

-2 sorry

Answer 11

(5/3, -2, 5)

Answer 12

What are your equations for the parametric form of the line?

Answer 13

i'm using the parametric equations above...then setting 6 = 1+3t, 6= -2t, 6 = 1+t and solving each for t

Answer 14

No, you're not thinking.

Answer 15

For each value of t
(x,y,z) = (1+3t, -2t, 1+t)
is a point on the line.

Answer 16

it cannot be that t is different for each ordinate; i.e., x doesn't have one value of t and y another etc.

Answer 17

Do you understand where that parametric form comes from?

Answer 18

okay...i just figured it out lol

Answer 19

So what's your final answer?

Answer 20

hang on i'm writing it out

Answer 21

on paper first

Answer 22

okay..so the line intersects the xy plane when z = 6 correct?

Answer 23

No. I recommend you go back and read the section in your book on the parametric form of lines.

Answer 24

or z = 0

Answer 25

No.

Answer 26

u get anywhere with it ska?

Answer 27

1+3t -2t + 1+t =6 ?

Then solve for t. when you solve t, plug it into this:

(1+3t, -2t, 1+t)

Answer 28

oh i have no idea...was just asking if you got anywhere with it...a shame he's the only one that can help with calc 3

Answer 29

What slaaibak suggests is exactly right.

You need to convince yourself that this makes sense.