If #A= <-5 ,-4 ,-1 ># and #B= <2 ,-9 ,8 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2016-10-13T21:00:44

#barA*barB - |barA||barB| ~~ -61.1#

For the dot-product of two vectors, one multiplies the corresponding components:

#barA*barB = (-5)(2) + (-4)(-9) + (-1)(8)#

#barA*barB = 18#

The magnitude of a vector is the square root of the sum of the squares of the components:

#|barA| = sqrt((-5)^2 + (-4)^2 + (-1)^2)#

#|barA| = sqrt(42)#

#|barB| = sqrt((2^2 + (-9)^2 + (8)^2)#

#|barB| = sqrt(149)#

#barA*barB - |barA||barB| = 18 - sqrt(42)sqrt(149)#

#barA*barB - |barA||barB| ~~ -61.1#