If #A= <6 ,9 ,-1 ># and #B= <9 ,-1 ,8 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2016-03-23T10:15:43

#A * B - ||A|| * ||B|| = 37 - sqrt(118)*sqrt(146)#

#A * B# is a dot product (or scalar product) and can be computed as follows:

#A = < color(blue)(6), color(green)(" "9), color(purple)(-1) >#
#B = < color(blue)(9), color(green)(-1), color(purple)(" "8) >#

#=> " " A * B = color(blue)(6 * 9) + color(green)(9 * (-1)) + color(purple)((-1) * 8) = 37#

#||A||# and #||B||# can be computed as follows:

#||A|| = sqrt(6^2 + 9^2 + (-1)^2) = sqrt(36 + 81 + 1) = sqrt(118)#

#||B|| = sqrt(9^2 + (-1)^2 + 8^2) = sqrt(81 + 1 + 64) = sqrt(146)#

In total, you have

#A * B - ||A|| * ||B|| = 37 - sqrt(118)*sqrt(146) ~~94,26#