If $A = < 6, - 4, - 1 >$ $A= <6 ,-4 ,-1 >$ and $B = < 2, - 9, 3 >$ $B= <2 ,-9 ,3 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Answer 1 · 2016-05-24T06:11:14

With the given data we start,

$A \cdot B = < 6 \cdot 2, (- 4) \cdot (- 9), (- 1) \cdot 3 >$ $A*B=<6*2,(-4)*(-9),(-1)*3>$

$A \cdot B = < + 12, + 36, - 3 >$ $A*B=<+12,+36,-3>$

$A \cdot B = 45$ $A*B=45$

$| | A | | = \sqrt{6^{2} + {(- 4)}^{2} + {(- 1)}^{2}}$ $||A||=sqrt(6^2+(-4)^2+(-1)^2)$

$| | A | | = \sqrt{36 + 16 + 1}$ $||A||=sqrt(36+16+1)$

$| | A | | = \sqrt{53}$ $||A||=sqrt(53)$

$| | A | | \approx 7.28$ $||A|| ~~7.28$

$| | B | | = \sqrt{2^{2} + {(- 9)}^{2} + 3^{2}}$ $||B||=sqrt(2^2+(-9)^2+3^2$

$| | B | | = \sqrt{94}$ $||B||=sqrt(94)$

$| | B | | \approx 9.70$ $||B|| ~~9.70$

Now lets plug in values

$A \cdot B - | | A | | | | B | | = 45 - (7.28) (9.70)$ $A*B -||A|| ||B||=45-(7.28)(9.70)$

$A \cdot B - | | A | | | | B | | = 45 - 70.616$ $A*B -||A|| ||B||=45-70.616$

$A \cdot B - | | A | | | | B | | = - 25.616$ $A*B -||A|| ||B||=-25.616$

If A= <6 ,-4 ,-1 >A=<6,−4,−1>A= <6 ,-4 ,-1 > and B= <2 ,-9 ,3 >B=<2,−9,3>B= <2 ,-9 ,3 >, what is A*B -||A|| ||B||A⋅B−||A||||B||A*B -||A|| ||B||?