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?

 

[Dick]

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.

 

[Calpalned]

I see thank you, Dick.

 

[Brian T]

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

 

[LCKurtz]

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

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

 

[Brian T]

 

[SammyS]

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