If $A = < 4, 3, - 1 >$ $A= <4, 3 ,-1 >$ and $B = < 8, 7, 6 >$ $B= <8 ,7 ,6 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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If $A = < 4, 3, - 1 >$ $A= <4, 3 ,-1 >$ and $B = < 8, 7, 6 >$ $B= <8 ,7 ,6 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Answer 1 · 2018-06-14T07:46:08

$A \cdot B - [A] [B] = - 18.6962$ $A·B-[A][B]=-18.6962$

Explanation:

$A = (4, 3, - 1)$ $A=(4,3,-1)$ and $B = (8, 7, 6)$ $B=(8,7,6)$ then dot product is

$A \cdot B = 32 + 21 - 6 = 47$ $A·B=32+21-6=47$

By other hand $[A] = \sqrt{4^{2} + 3^{2} + 1^{2}} = \sqrt{26}$ $[A]=sqrt(4^2+3^2+1^2)=sqrt26$
$[B] = \sqrt{8^{2} + 7^{2} + 6^{2}} = \sqrt{166}$ $[B]=sqrt(8^2+7^2+6^2)=sqrt166$

$A \cdot B - [A] [B] = 47 - \sqrt{26} \sqrt{166} = 47 - 65.6962 = - 18.6962$ $A·B-[A][B]=47-sqrt26sqrt166=47-65.6962=-18.6962$

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If $A = < 4, 3, - 1 >$ $A= <4, 3 ,-1 >$ and $B = < 8, 7, 6 >$ $B= <8 ,7 ,6 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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If A=<4,3,−1>A= <4, 3 ,-1 > and B=<8,7,6>B= <8 ,7 ,6 >, what is A⋅B−||A||||B||A*B -||A|| ||B||?

1 Answer

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If $A = < 4, 3, - 1 >$ $A= <4, 3 ,-1 >$ and $B = < 8, 7, 6 >$ $B= <8 ,7 ,6 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?