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answer is no intersection / skew lines but how?!
yay amistre :D !
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
how do you prove that mathematically. i do understand that concept that you just mentioned
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) ? !
that is how far i have went ... just stuck at that step
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
kay take your time boss :)
when lines intersect... (x-3,y-20,z-7) = t(2,-4,5) ter ?ter? whats this?
its one of the two equationse that intersect .. the format of this eqaution has confused memyself
whats the ?ter? mean i take it its a typo of some kind
ter means where value of t can me any real number sorry .. u knw like xer
(x-5)/2 = y-2 = (z+4)/-3 a=2; b=1 ; c=-3 ; just the denoms of your things here right?
t<2,1,-3> is the vector and P(5,2,-4)
yeah denoms are right
x = 5 +2t y = 2 + t z = -3 -4t for our equation of a line in R^3 or at least one of them
you mean z = -4-3t ?
(x-3,y-20,z-7)=t(2,-4,5) x= 3 +2t y= 20 -4t z= 7 +5t is our other line right?
yeah :) lol
hmm but how did you get that parametric equation ... you just diregarded x- y- etc?
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
x-3 means x = 3 + vector x component
x-x0 = Vx x = x0 + Vx
oh true indeed
5 +2t = 3 +2s 2 + t = 20 -4s -4 -3t = 7+5s
solve for s and t and see if they match in the 3rd spot
hmm :O i can work the rest you can help other people as with with great power comes great responsibilities :P
if i start sticking to the walls ........
it prolly means i need a bath lol
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
GOT IT YAY :) ! Love you man .. studying to get int queens university bro :(
i got it just got to maintain their conditional offer :)