# Find two vectors perpendicular to a line

• Jan 21st 2011, 12:09 PM
nautica17
Find two vectors perpendicular to a line
This is a question from my calculus 3 class.

"Find two unit vectors in 2-space that are perpendicular to the line y = -5x + 1"

I have to do this without a dot product or any matrices. And so I'm lost as to what I have to do. Where do I begin is what I'm asking? I'm thinking I maybe have to make an initial vector along the line and then go from there? It's the rotation part that's tripping me up though.
• Jan 21st 2011, 12:18 PM
Plato
Quote:

Originally Posted by nautica17
"Find two unit vectors in 2-space that are perpendicular to the line y = -5x + 1"

You know that the slope of the line is $\displaystyle -5$ and the point $\displaystyle (0,1)$ is on the line.
The slope of the perpendicular is $\displaystyle \frac{1}{5}$.
Find two points one on each side of the line such that they and $\displaystyle (0,1)$ determine a slope of $\displaystyle \frac{1}{5}$.
Make unit vectors out of that.
• Jan 21st 2011, 12:21 PM
nautica17
Okay, thank-you, I'll work on that. :)
• Jan 21st 2011, 12:31 PM
nautica17
Edit: nevermind.