If $A = < - 5, 6, - 3 >$ $A= <-5 ,6 ,-3 >$ and $B = < - 6, - 4, 4 >$ $B= <-6 ,-4 ,4 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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If $A = < - 5, 6, - 3 >$ $A= <-5 ,6 ,-3 >$ and $B = < - 6, - 4, 4 >$ $B= <-6 ,-4 ,4 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Answer 1 · 2016-07-18T13:31:20

$\approx - 75$ $~~-75$

Explanation:

$A \cdot B = (- 5 \cdot - 6) + (6 \cdot - 4) + (- 3 \cdot 4) = - 6$ $A*B = (-5*-6) + (6*-4)+ (-3*4) = -6$
$| | A | | = \sqrt{{(- 5)}^{2} + {(6)}^{2} + {(- 3)}^{2}} = \sqrt{70}$ $||A|| = sqrt((-5)^2 + (6)^2+ (-3)^2) = sqrt(70)$
$| | B | | = \sqrt{{(- 6)}^{2} + {(- 4)}^{2} + {(4)}^{2}} = \sqrt{68}$ $||B|| = sqrt((-6)^2 + (-4)^2+ (4)^2) = sqrt68$

putting it together

$A \cdot B - | | A | | | | B | | = - 6 - \sqrt{70 \cdot 68} \approx - 75$ $A*B-||A||||B|| =-6 - sqrt(70*68) ~~-75$

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If $A = < - 5, 6, - 3 >$ $A= <-5 ,6 ,-3 >$ and $B = < - 6, - 4, 4 >$ $B= <-6 ,-4 ,4 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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If A= <-5 ,6 ,-3 >A=<−5,6,−3>A= <-5 ,6 ,-3 > and B= <-6 ,-4 ,4 >B=<−6,−4,4>B= <-6 ,-4 ,4 >, what is A*B -||A|| ||B||A⋅B−||A||||B||A*B -||A|| ||B||?

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If $A = < - 5, 6, - 3 >$ $A= <-5 ,6 ,-3 >$ and $B = < - 6, - 4, 4 >$ $B= <-6 ,-4 ,4 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?