# Determining if a line is perpendicular in ##R^3##

• Calpalned

## Homework Statement

Is the line through (-2, 4, 0) and (1, 1, 1) perpendicular to the line through (2, 3, 4) and (3, -1, -8)?

## Homework Equations

R = R0 + tV (for each line)

## The Attempt at a Solution

If the lines are parallel, then the V for the two equations will be proportional to each other. How are the two V's related if they are perpendicular?

## Homework Statement

Is the line through (-2, 4, 0) and (1, 1, 1) perpendicular to the line through (2, 3, 4) and (3, -1, -8)?

## Homework Equations

R = R0 + tV (for each line)

## The Attempt at a Solution

If the lines are parallel, then the V for the two equations will be proportional to each other. How are the two V's related if they are perpendicular?

Think dot product.

I see thank you, Dick.

You could also use the cross product if you prefer that.

You could also use the cross product if you prefer that.

And you don't mind doing at least three times as much work...

You might also want to be sure that the lines intersect and thus are not skew lines.