- #1

paulrb

- 18

- 1

## Homework Statement

Show that the lines given by the equation ax + by + c = 0 and bx - ay + d = 0 (where a, b, c, d are in R) are perpendicular by finding a vector in the direction of each line and showing that these vectors are orthogonal. (Hint: Watch out for the cases in which a or b equals zero.)

## Homework Equations

Vectors a and b are orthogonal if the dot product of a and b are 0.

## The Attempt at a Solution

I have spent a long time trying to figure out this problem but I don't even know how to start. I don't know how to create a vector in the same direction as a line unless I know 2 points on the line or the slope of the line. In this case I don't know either because the equation is so general. That is, unless choosing my own values of a, b, and c is acceptable (Is it?).

I cannot use many techniques to prove this since not much has been introduced in the course. Only basic vector properties, the dot product, and projections have been introduced so far.