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

## 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?

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Dick
Homework Helper

## 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.

LCKurtz
Homework Helper
Gold Member
You could also use the cross product if you prefer that.
And you don't mind doing at least three times as much work...

SammyS
Staff Emeritus