If $A= <2 ,6 ,-3 >$ and $B= <3, -5, 3 >$ , what is $A*B -||A|| ||B||$ ?

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Answer 1 · 2016-09-20T08:26:19

$- 33 - 7 sqrt(43)$

We have: $A = <2, 6, - 3>$ and $B = <3, - 5, 3>$

$=> A cdot B - abs(A) abs(B) = <2, 6, - 3> cdot <3, - 5, 3> - abs(<2, 6, - 3>) abs(<3, - 5, 3>)$

$=> A cdot B - abs(A) abs(B) = (2 cdot 3) + (6 cdot (- 5)) + ((- 3) cdot 3) - sqrt(2^(2) + 6^(2) + (- 3)^(2)) cdot sqrt(3^(2) + 5^(2) + 3^(2))$

$=> A cdot B - abs(A) abs(B) = 6 - 30 - 9 - sqrt(4 + 36 + 9) cdot sqrt(9 + 25 + 9)$

$=> A cdot B - abs(A) abs(B) = - 33 - sqrt(49) cdot sqrt(43)$

$=> A cdot B - abs(A) abs(B) = - 33 - 7 sqrt(43)$

If A= <2 ,6 ,-3 >A= <2 ,6 ,-3 > and B= <3, -5, 3 >B= <3, -5, 3 >, what is A*B -||A|| ||B||A*B -||A|| ||B||?