# Thread: vector-equation of straight line

1. ## vector-equation of straight line

can i do this question in both ways? since the question does not state which point is a , (r=a+tb ) , and how about the b , can i take (3,1, -2 ) minus (4, 0 ,2 ) and (4, 0 ,2 ) minus (3,1, -2)

2. ## Re: vector-equation of straight line

Originally Posted by delso
can i do this question in both ways? since the question does not state which point is a , (r=a+tb ) , and how about the b , can i take (3,1, -2 ) minus (4, 0 ,2 ) and (4, 0 ,2 ) minus (3,1, -2)
Good morning,

if you have 2 points then you can get 4 different equations which describe exactly the same straight line. Using your points A(3,1,-0) and B(4,0,2) with the stationary vectors $\displaystyle \vec a = \overrightarrow{OA}$ and $\displaystyle \vec b = \overrightarrow{OB}$ you'll get:

$\displaystyle l: \vec r = \vec a + \lambda(\vec b - \vec a)$

$\displaystyle l: \vec r = \vec a + \sigma( \vec a- \vec b )$

$\displaystyle l: \vec r = \vec b + \tau(\vec b - \vec a)$

$\displaystyle l: \vec r = \vec b + \rho( \vec a- \vec b )$