Determine the point of intersection between the lines (x-3,y-20,z-7)=t(2,-4,5) ter, and (x-5)/2 = y-2 = (z+4)/-3 - AMISTRE64 HELP PLEASE!

- anonymous

- chestercat

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- anonymous

answer is no intersection / skew lines but how?!

- anonymous

yay amistre :D !

- amistre64

since they are in 3d space; they can look to cross, but actually never touch. such as the line in the ceiling and the line on the floor both make it to a corner but never intersect each other

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- anonymous

how do you prove that mathematically. i do understand that concept that you just mentioned

- anonymous

i can get the second equation in terms of x y and z
but how do i sub that in to the second equation and how do i deal with t(2,-4,5) ? !

- anonymous

that is how far i have went ... just stuck at that step

- amistre64

we prove it by seeing if the scalar for one line vector equates to the scalar in the other ... but i gotta review it real quick to recall some details

- anonymous

kay take your time boss :)

- amistre64

when lines intersect...
(x-3,y-20,z-7) = t(2,-4,5) ter ?ter? whats this?

- anonymous

its one of the two equationse that intersect .. the format of this eqaution has confused memyself

- amistre64

whats the ?ter? mean i take it its a typo of some kind

- anonymous

ter means where value of t can me any real number sorry .. u knw like xer

- amistre64

(x-5)/2 = y-2 = (z+4)/-3
a=2; b=1 ; c=-3 ; just the denoms of your things here right?

- amistre64

t<2,1,-3> is the vector and P(5,2,-4)

- anonymous

yeah denoms are right

- amistre64

x = 5 +2t
y = 2 + t
z = -3 -4t
for our equation of a line in R^3 or at least one of them

- anonymous

you mean z = -4-3t ?

- amistre64

(x-3,y-20,z-7)=t(2,-4,5)
x= 3 +2t
y= 20 -4t
z= 7 +5t
is our other line right?

- amistre64

yeah :) lol

- anonymous

hmm but how did you get that parametric equation ... you just diregarded x- y- etc?

- amistre64

now we equate our x=x but use a different variable to indicate our scalar; say s instead of t and solve for the system of equations

- amistre64

x-3 means x = 3 + vector x component

- amistre64

x-x0 = Vx
x = x0 + Vx

- anonymous

oh true indeed

- amistre64

5 +2t = 3 +2s
2 + t = 20 -4s
-4 -3t = 7+5s

- amistre64

solve for s and t and see if they match in the 3rd spot

- anonymous

hmm :O i can work the rest you can help other people as with with great power comes great responsibilities :P

- amistre64

if i start sticking to the walls ........

- amistre64

it prolly means i need a bath lol

- anonymous

lmfao xD

- amistre64

if the system of equations creates s and t to meet at a common point; then they intersect there; if not then they never meet

- anonymous

GOT IT YAY :) ! Love you man .. studying to get int queens university bro :(

- anonymous

i got it just got to maintain their conditional offer :)

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