# Thread: Equation of a line

1. ## Equation of a line

Find vector equation for line

2x-3y=1

Can the answer be r=(1,1) + t(1,-2)

Another important question will there always be an infinate number of answers for these questions??

and any good tips to find vector equation of a line or even of a plane

2. Originally Posted by someone21
Find vector equation for line

2x-3y=1

Can the answer be r=(1,1) + t(1,-2) Mr F says: Clearly not. t = 0 => r = i + j and the point given by this position vector, (1, 1), certainly doesn't lie on the line. However, r = 2 i + j + t (3 i + 2 j) is an answer ......

Another important question will there always be an infinate number of answers for these questions?? Mr F says: Yes. For a line in the xy-plane, the answer has the form r = a i + b j + t (c i + d j) where (a, b) is any point on the line and c i + d j is any vector in the direction of the line. And there are an infinite number of points n the line ......

and any good tips to find vector equation of a line or even of a plane Mr F says: Study as many examples as possible. Starting with the examples given in your class notes and textbook.
..

3. Originally Posted by mr fantastic
..

tying mistake

r=(-1,-1)+ t(3,2)

4. Originally Posted by someone21
tying mistake

r=(-1,-1)+ t(3,2)