If $A= <2 ,1 ,-3 >$ and $B= <-6 ,-4 ,0 >$ , what is $A*B -||A|| ||B||$ ?

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Answer 1 · 2018-07-05T07:33:16

$=> color(indigo)(-42.9815$

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

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

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

$color(green)(vecA·vecB=2 * -6 + 1 * -4 + -3·0= -16$

$color(blue)(abs(vecA)=sqrt(2^2+1^2+ -3^2)=sqrt 14$

$color(blue)(abs(vecB)=sqrt(-6^2+ -4^2+ 0^2)=sqrt 52$

$vecA·vecB-abs(vecA)·abs(vecB)=-16- sqrt 14 sqrt 52$

$=> -16 -26.9815 =color(indigo)(-42.9815$

If A= <2 ,1 ,-3 >A= <2 ,1 ,-3 > and B= <-6 ,-4 ,0 >B= <-6 ,-4 ,0 >, what is A*B -||A|| ||B||A*B -||A|| ||B||?