Question

Consider the line that passes through the point and is parallel to the given vector.
(1, -5, 9)
‹-1, 2, -3›

(a) Find symmetric equations for the line.

Answer 1

x= -1t+1
y=2t-5
z= -3t+9

Answer 2

this is parametric, we want symmetric,

Answer 3

x-1=-t
-x+1=t

Answer 4

y+5=2t

(y+5)/2 =t

Answer 5

so, how do you get parametric eq's out of that? and then symmetric is just parametric solved for t?

Answer 6

yes, solve for t to get symmetric

Answer 7

Example
------------
vector <a,b,c>
point <p,q,r>

x= at +p
y= bt+q
z= ct+ r

Answer 8

awesome.

Answer 9

so t=(z-9)/-3

Answer 10

yes

Answer 11

yep, a line is just a vector add to a point.

Answer 12

since the vector can be any scaled version of itself; we use a "t" to indicate that any size of this vector is sufficient to produce a line