Calc III: Shortest Distance in 3D Problem

[nchin]

Calculus III, find shortest distance, 3 dimension problem? check my answer please??

What is the shortest distance from the point P = (0, 1, 2) to the line given by l(t) = (1+t, 2-2t, 3+3t)?

use distance formula

d = sqrt ((x-0)^(2) + (y-1)^(2) + (z-2)^(2))

d^(2) = ((x)^(2) + (y-1)^(2) + (z-2)^(2))

substitute l(t) values

=((1+t)^(2) + (1-2t)^(2) + (1+3t)^(2))

simplify

l ' (t) = 2 + 2t + 8t - 4 +6 + 18t

= 2 + 2t + 8t - 4 + 6 + 18t

=28t + 4

4(1+7t) = 0

t = - 1/7What do i do after i find the t value?

 

[LCKurtz]

What is the shortest distance from the point P = (0, 1, 2) to the line given by l(t) = (1+t, 2-2t, 3+3t)?

use distance formula

d = sqrt ((x-0)^(2) + (y-1)^(2) + (z-2)^(2))

d^(2) = ((x)^(2) + (y-1)^(2) + (z-2)^(2))

substitute l(t) values

=((1+t)^(2) + (1-2t)^(2) + (1+3t)^(2))

simplify

l ' (t) = 2 + 2t + 8t - 4 +6 + 18t

= 2 + 2t + 8t - 4 + 6 + 18t

=28t + 4

4(1+7t) = 0

t = - 1/7


What do i do after i find the t value?

I didn't check your work, but the t value will tell you what point on the line is closest. Then what?

 

[nchin]

I didn't check your work, but the t value will tell you what point on the line is closest. Then what?

nvm my whole answer is wrong. i used the wrong formula. i figured it out thanks.