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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.Quote:
Originally Posted by kenshinofkin
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.