Consider the line which passes through the point P(-3, 5, 1), and which is parallel to the line x=1+6t,y=2+5t,z=3+4t Find the point of intersection of this new line with each of the coordinate planes: I've got + t so far, but not sure where really to go from there.

Question

Consider the line which passes through the point P(-3, 5, 1), and which is parallel to the line x=1+6t,y=2+5t,z=3+4t Find the point of intersection of this new line with each of the coordinate planes: I've got <1,2,3> + t<6,5,4> so far, but not sure where really to go from there.

anonymous · Answer

someone????  anyone??????  seriously??????  due in like a few hours................and this is only question 5 of 20.........................

anonymous · Answer

tried moving on, but now i'm also stuck on another problem because these stupid questions aren't explained in the stupid book that i paid 200 stupid bucks for!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

rational · Answer

where are you stuck

anonymous · Answer

i said where i was stuck......said this is what i have, don't know where to go from there.

anonymous · Answer

@True_Alpha_Wolf    @Jman00000   @surd   @Punkchick   @chainedecho

rational · Answer

the required line is <-3, 5, 1> + t<6,5,4> right ?

true_alpha_wolf · Answer

im bad at math

anonymous · Answer

ready to cry or stab myself in the eye with my pencil here.  first i deal with someone cursing me out for no reason, then nothing at all

anonymous · Answer

y u mention me dafuq

anonymous · Answer

I sorry thought she could use the help

rational · Answer

you did not reply me properly in previous thread

anonymous · Answer

no, i had <1,2,3> + t<6,5,4>

anonymous · Answer

i'm sorry, @rational, i wasn't gonna sift through that garbage that other person was posting.  i just ignored it and posted again

rational · Answer

thats the given line

anonymous · Answer

i'm already having a bad day and if i'd read the obscenities that guy was throwing around, i would have lost it.

rational · Answer

a line parallel to this will be having same direction vector, yes ?

rational · Answer

you're free to ignore him

anonymous · Answer

bye bye

anonymous · Answer

Tourists who had paid money for a safari were packed into the bus like sardines in a can.

Which statement is true?

 The sentence features figurative language in the form of a metaphor.

 The sentence features figurative language in the form of a simile.

 The sentence features literal language in the form of a metaphor.

 The sentence features literal language in the form of simile.

rational · Answer

we're talking about some spammer who bugged us in the previous thread @sambolin1996

anonymous · Answer

oh lol

rational · Answer

anyways, did you get the direction vector concept ? @saiken2009

anonymous · Answer

i don't get it, why is my thing wrong?  i did it just how the book told me to do it.

anonymous · Answer

Hey I was just trying to help  :(

rational · Answer

all parallel lines will have same direction vector

anonymous · Answer

and the x0+at is there

anonymous · Answer

x0+at, etc, +t

rational · Answer

given line : <1,2,3> + t<6,5,4> a line parallel to this line will be of form + t<6,5,4> yes?

anonymous · Answer

so if we have 1+6t=x, x0 should be 1 and a should be 6

rational · Answer

you're right

rational · Answer

see if u can answer my q above

anonymous · Answer

umm....

anonymous · Answer

ok, so yeah.  i guess.

anonymous · Answer

little lost on this whole section.  sorry if i'm a little slow.

rational · Answer

+ t<6,5,4> since you know that the line passes throughP(-3, 5, 1), the equation would be : <-3, 5, 1> + t<6,5,4>

rational · Answer

its okay..

anonymous · Answer

so we just change the point of origin?

rational · Answer

yes, parallel lines will have same direction.
just the point changes

anonymous · Answer

it's another line and the second part of that (the a, b, c) is just the vector that says the direction and mag and the point in the beginning (the x0, y0, z0) gives us a point in the space for the vector

anonymous · Answer

am i understanding that right?

rational · Answer

yes :
a line can be represented using a "point" and a "direction vector"

|dw:1410353078067:dw|

rational · Answer

for parallel lines,
direction vector will be same

only the point changes

anonymous · Answer

so the line i'm actually focusing on is <-3, 5, 1> +t<6,5,4>

rational · Answer

yes <-3, 5, 1> + t<6,5,4> and any point on this line will be : (-3+6t, 5+5t, 1+4t)

anonymous · Answer

and i know the xy plane coordinate will be (_, _, 0) and the xz will be (_,0,_).

rational · Answer

Correct !
for the intersection point with xy plane, 
simply set your z coordiante to 0 and solve t

rational · Answer

(-3+6t, 5+5t, `1+4t`)

rational · Answer

set that equal to 0 and solve t

anonymous · Answer

that gives me t though.  how does that give me the x, y points in the plane?

rational · Answer

plug that t in the point again :

(-3+6t, 5+5t, 1+4t)

anonymous · Answer

oh, so plug in -4 for the other two then.

rational · Answer

1+4t = 0
t = ?

anonymous · Answer

and so on for the other planes?  but with different zeros

anonymous · Answer

ok, this is nowhere in my book and my teacher didn't do this.  so frustrating.

rational · Answer

i knw

anonymous · Answer

and since i have a headache, that should have been -1/4 instead of t=4

anonymous · Answer

oops

rational · Answer

(-3+6t, 5+5t, 1+4t)

you should get below intersecting points :
xy plane :  (-9/2, 15/4, 0)
yz plane : (0, 15/2, 3)
zx plane : (-9, 0, -3)

anonymous · Answer

thanks.  @rational