# Perpendicular lines

• Apr 17th 2008, 01:42 AM
kenshinofkin
Perpendicular lines
This problem wasn't assigned to my class and is an even number so I wanted to make sure I was correct or even on the right track.

Is line through (4, 1, -1) and (2, 5, 3) perpendicular to the line through (-3, 2, 0) and (5, 1, 4)?

My solution:

A = < 2 - 4, 5 - 1, 3 - -1>
= <-2,4,4>
B = <5 - -3, 1 - 2, 4 - 0>
= <8,-1,4>

A X B = <20,40,-30>

<-2,4,4><20,40,-30> = 0
<8,-1,4><20,40,-30> = 0

They are perpendicular.
• Apr 17th 2008, 01:51 AM
mr fantastic
Quote:

Originally Posted by kenshinofkin
This problem wasn't assigned to my class and is an even number so I wanted to make sure I was correct or even on the right track.

Is line through (4, 1, -1) and (2, 5, 3) perpendicular to the line through (-3, 2, 0) and (5, 1, 4)?

My solution:

A = < 2 - 4, 5 - 1, 3 - -1>
= <-2,4,4>
B = <5 - -3, 1 - 2, 4 - 0>
= <8,-1,4>

A X B = <20,40,-30>

<-2,4,4><20,40,-30> = 0
<8,-1,4><20,40,-30> = 0

They are perpendicular.

A and B are vectors in the direction of the two lines.

A.B = <-2,4,4> <8,-1,4> != 0 therefore the lines are >not< perpendicular.

Note:

A x B gives a vector perpendicular to A and B. I don't know why you've found it - it's irrelevant and has in fact completely mislead you into making a mistake.

Because A x B is perpendicular to A and B it's no surprise that you get

<-2,4,4><20,40,-30> = 0

and

<8,-1,4><20,40,-30> = 0.

These results have absolutely nothing to do with the question.