# dot product of vecotrs

Question:
Find (3a+b)dot(2b-4a) if a=-i-3j+k and b=2i+4j-5k

I did:
=3(-1,-3,1)+(2,4,-5)dot 2(2,4,-5)-4(-1,-3,1)
=(-3,-9,3)+(2,4,-5)dot(4,8,-10)-(4+12,-4)
=(-1,-5,-2)dot(0,-4,-6)
=(0,20,12)
=0+20+12
=32

The text book answer is -80. What did I do wrong/

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1. oops. Flipped a sign:

=3(-1,-3,1)+(2,4,-5)dot 2(2,4,-5)-4(-1,-3,1)
=(-3,-9,3)+(2,4,-5)dot(4,8,-10)+(4+12,-4)
=(-1,-5,-2)dot(8,20,-14)
= -8-100+28
= -80

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2. Sure looks like you corrected the typo, but made no effort to adjust the corresponding arithmetic.
http://www.jiskha.com/display.cgi?id=1423332996
The unnecessary duplication of work could have been avoided.

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