If $A = < - 2, - 5, 3 >$ $A= <-2 ,-5 ,3 >$ and $B = < - 7, 4, - 9 >$ $B= <-7 ,4 ,-9 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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If $A = < - 2, - 5, 3 >$ $A= <-2 ,-5 ,3 >$ and $B = < - 7, 4, - 9 >$ $B= <-7 ,4 ,-9 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Answer 1 · 2016-04-08T18:56:46

$A \cdot B - | | A | | | | B | | = - 107, 48$ $A*B-||A|| ||B||=-107,48$

Explanation:

$A = < - 2, - 5, 3 >$ $A= <-2,-5,3>$
$B = < - 7, 4, - 9 >$ $B= <-7,4,-9>$

$let's find ||A||$ $"let's find ||A||"$

$| | A | | = \sqrt{A_{x}^{2} + A_{y}^{2} + A_{z}^{2}}$ $||A||=sqrt(A_x^2+A_y^2+A_z^2)$
$| | A | | = \sqrt{{(- 2)}^{2} + {(- 5)}^{2} + 3^{2}}$ $||A||=sqrt((-2)^2+(-5)^2+3^2)$
$| | A | | = \sqrt{4 + 25 + 9}$ $||A||=sqrt(4+25+9)$
$| | A | | = \sqrt{38}$ $||A||=sqrt38$

$let's find ||B||$ $"let's find ||B||"$

$| | B | | = \sqrt{B_{x}^{2} + B_{y}^{2} + B_{z}^{2}}$ $||B||=sqrt(B_x^2+B_y^2+B_z^2)$
$| | B | | = \sqrt{{(- 7)}^{2} + 4^{2} + {(- 9)}^{2}}$ $||B||=sqrt((-7)^2+4^2+(-9)^2)$
$| | B | | = \sqrt{49 + 16 + 81}$ $||B||=sqrt(49+16+81)$
$| | B | | = \sqrt{146}$ $||B||=sqrt(146)$

$let's find A \cdot B$ $"let's find " A*B$

$A \cdot B = A_{x} \cdot B_{x} + A_{y} \cdot B_{y} + A_{z} \cdot B_{z}$ $A*B=A_x*B_x+A_y*B_y+A_z*B_z$

$A \cdot B = 14 - 20 - 27$ $A*B= 14-20-27$
$A \cdot B = - 33$ $A*B=-33$

$A \cdot B - | | A | | | | B | | = - 33 - (\sqrt{38} \cdot \sqrt{146})$ $A*B-||A|| ||B||=-33-(sqrt38*sqrt146)$

$A \cdot B - | | A | | | | B | | = - 33 - \sqrt{5548}$ $A*B-||A|| ||B||=-33-sqrt5548$
$A \cdot B - | | A | | | | B | | = - 33 - 74, 48$ $A*B-||A|| ||B||=-33-74,48$
$A \cdot B - | | A | | | | B | | = - 107, 48$ $A*B-||A|| ||B||=-107,48$

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If $A = < - 2, - 5, 3 >$ $A= <-2 ,-5 ,3 >$ and $B = < - 7, 4, - 9 >$ $B= <-7 ,4 ,-9 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Explanation:

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If A=<−2,−5,3>A= <-2 ,-5 ,3 > and B=<−7,4,−9>B= <-7 ,4 ,-9 >, what is A⋅B−||A||||B||A*B -||A|| ||B||?

1 Answer

Explanation:

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If $A = < - 2, - 5, 3 >$ $A= <-2 ,-5 ,3 >$ and $B = < - 7, 4, - 9 >$ $B= <-7 ,4 ,-9 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?