Math Is Fun Forum

Shelled

Member

Registered: 2014-04-15

Posts: 44

Distance between point and line

find the distance between the line r(t)= (1+t, 2-2t, -1+4t) and point (1,0,1)

With the above problem, I attempted it and thought I had a good idea of how to solve it, but the anwer I'm getting is different from the one that they've given.
Could someone help me find where i went wrong?

so, I calculated the distance between these two as
(1+t-1, 2-2t-0, -1+4t-1) = (t, 2-2t, 2+4t)

and then to find the value of t, from the equation of the line, i took d= (1, -2, 4)

and since these two are orthogonal, calculated the dot product of (t, 2-2t, 2+4t) and (1, -2, 4) and solved for t to get t=-4/21
and then from that length of t as (-4/21)^2 and squared it to get t=4/21

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Distance between point and line

Hi;

I am getting

with a minimum distance of

This assumes

find the distance between the line r(t)= (1+t, 2-2t, -1+4t) and point (1,0,1)

that you meant shortest distance.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,635

Re: Distance between point and line

hi Shelled,

Your method is right.  Here's my calculation:

(t, 2-2t, 4t-2) . (1, -2, 4) = t -4 + 4t + 16t -8 = 0  ... 21t - 12 = 0  ... t = 4/7

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,438

Website

Re: Distance between point and line

find the distance between the line r(t)= (1+t, 2-2t, -1+4t) and point (1,0,1)

With the above problem, I attempted it and thought I had a good idea of how to solve it, but the anwer I'm getting is different from the one that they've given.
Could someone help me find where i went wrong?

so, I calculated the distance between these two as
(1+t-1, 2-2t-0, -1+4t-1) = (t, 2-2t, 2+4t)

and then to find the value of t, from the equation of the line, i took d= (1, -2, 4)

and since these two are orthogonal, calculated the dot product of (t, 2-2t, 2+4t) and (1, -2, 4) and solved for t to get t=-4/21
and then from that length of t as (-4/21)^2 and squared it to get t=4/21

Check the bolded.

Shelled

Member

Registered: 2014-04-15

Posts: 44

Re: Distance between point and line

Thanks for the help
wasn't careful with the signs