Question

Use set theory or vector notation to describe the points that lie on the given configuration:: The line passing through ( 0,2,1 ) in the direction of 2i-k.

Answer 1

is it l(t) = (2t)i + 2j + (1-t)k ???

Answer 2

Here are some notes
http://tutorial.math.lamar.edu/Classes/CalcIII/EqnsOfLines.aspx

Answer 3

I think like this: P (for point on the line) is P0 (starting point) + k* direction
P= P0 + k D

here P0 is ( 0,2,1 )
the direction vector D is (2,0,-1)

so P= (0,2,1) + k(2,0,-1)

Answer 4

you can use i , j , k instead:
P = 0*i + 2*j +1*k + t*2i + t*0j + t*-1k (I switched to using t instead of k, because is now a basis. up above k was just some number)

simplify to get
P= 2t i + 2j + (1-t) k

Answer 5

excellent, so i got it correct

Answer 6

in your first message ( p= 2ti....) what form/notation would you call that?

Answer 7

I always find it easier to remember the vector way: start point + t*direction vector
you always need a starting point, and it makes sense to add in a direction that you move along however far (using t)

Answer 8

thank you kindly

Answer 9

Paul's notes show how to write this in parametric form or as symmetric equations of a line