If #A= <-5 ,3 ,-3 ># and #B= <2 ,2 ,8 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2016-12-28T02:46:11

#A*B-||A||||B|| = -28-6sqrt(86)~~-83.64#

Given vectors #vec(x) = <x_1, x_2, x_3># and #vec(y) = <y_1, y_2, y_3>#, we have

#vec(x)*vec(y) = x_1y_1+x_2y_2+x_3y_3#

and

#||vec(x)|| = sqrt(x_1^2+x_2^2+x_3^2)#

Using these on the given vectors, we have

#A*B = -5(2)+3(2)+(-3)(8) = -10+6-24 = -28#

and

#||A||||B|| = sqrt((-5)^2+3^2+(-3)^2)*sqrt(2^2+2^2+8^2)#

#=sqrt(43)*sqrt(72)#

#=6sqrt(86)#

so, taken together

#A*B-||A||||B|| = -28-6sqrt(86)~~-83.64#