If $A = < 7, - 5, 1 >$ $A= <7 ,-5 ,1 >$ and $B = < 4, 1, 3 >$ $B= <4 ,1 ,3 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Answer 1 · 2017-01-03T17:53:51

$\sqrt{26} (\sqrt{26} - \sqrt{75})$ $sqrt26 (sqrt 26 - sqrt 75)$

$A . B = 7 \cdot 4 + (- 5) \cdot 1 + 1 \cdot 3$ $A.B= 7*4 +(-5)*1 +1*3$ =26

$| | A | | = \sqrt{7^{2} + {(- 5)}^{2} + 1^{2}} = \sqrt{75}$ $||A||= sqrt (7^2 + (-5)^2 + 1^2)= sqrt75$

$| | B | | = \sqrt{4^{2} + 1^{2} + 3^{2}} = \sqrt{26}$ $||B||= sqrt (4^2 +1^2 +3^2)= sqrt 26$

The given expression would therefore equal to $26 - \sqrt{75} \sqrt{26}$ $26-sqrt75 sqrt26$

= $\sqrt{26} (\sqrt{26} - \sqrt{75})$ $sqrt26 (sqrt 26 - sqrt 75)$

If A=<7,−5,1>A= <7 ,-5 ,1 > and B=<4,1,3>B= <4 ,1 ,3 >, what is A⋅B−||A||||B||A*B -||A|| ||B||?