Find Point on 3D Line Through Given Coordinates

[Bucky]

As part of a larger question, i need to find a point the following line goes through:


r = -i + 2j + k + t(i-2k)

I have rearranged it into an alternative form (as per my notes) as

r = (t-1) i + 2j + (1-2t) k

i am supposed to be able to find a point the line passes through from this but i just can't see it, can someone help me out?

 

[NateTG]

What happens when t=0 or t=1?

 

[Bucky]

see that was what i was trying to think in terms of...but i couldn't see how there were two "limiting vectors" that defined the line.

if t=0 you get

-i+2j+k

and if t=1

2j-k


i can't help but think that these are significant somehow...

 

[neutrino]

see that was what i was trying to think in terms of...but i couldn't see how there were two "limiting vectors" that defined the line.

if t=0 you get

-i+2j+k

and if t=1

2j-k


i can't help but think that these are significant somehow...

Those are the position vectors of the two points, for t=0 and t=1, through which the line described by r passes.

 

[Bucky]

ah i think i get it. thank you very much for the help.