If #A= <2 ,7 ,-4 ># and #B= <-2 ,-1 ,5 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2018-07-05T07:20:14

#color(crimson)(- 71.2492)#

#"Dot Product or Scalar Product " #
#(a_1,a_2,a_3)·(b_1,b_2,b_3)=a_1b_1+a_2b_2+a_3b_3#

#"Vector Product " = abs(vec A) * abs(vec B)#

![https://sites.google.com/a/g.coppellisd.com/coppell-ib-math/math-sl/topics---sl/vectors/scalar-and-vector-product]( useruploads.socratic.org )

#color(purple)(vecA·vecB=2 * -2 + 7 * -1 + -4·5=-31#

#color(blue)(abs(vecA)=sqrt(2^2+7^2+ -1^2)=sqrt 54#

#color(blue)(abs(vecB)=sqrt(-2^2+ -1^2+ 5^2)=sqrt 30#

Finally: #vecA·vecB-abs(vecA)·abs(vecB)=-21- sqrt54 sqrt 30#

#=> -31 -40.2492 =color(crimson)(-71.2492#