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

$color(crimson)(- 71.2492)$

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

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

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

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

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

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

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

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