If $A = < - 2, 3, 3 >$ $A= <-2 ,3 ,3 >$ and $B = < - 9, 4, 8 >$ $B= <-9 ,4 ,8 >$ , what is $A \cdot B - | | A | | | | B | |$ $A*B -||A|| ||B||$ ?

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Answer 1 · 2017-02-24T12:15:39

5.514

Dot product A.B=(-2)(-9)+(3)(4)+(3)(8) = 54

$| | A | | = \sqrt{{(- 2)}^{2} + 3^{2} + 3^{2}} = \sqrt{22}$ $||A||= sqrt((-2)^2+3^2 +3^2)=sqrt22$

$| | B | | = \sqrt{{(- 9)}^{2} + 4^{2} + 8^{2}} = \sqrt{161}$ $||B||= sqrt((-9)^2+ 4^2+8^2)=sqrt161$

Therefore $A . B - | | A | | | | B | | = 54 - \sqrt{22} \sqrt{161}$ $A.B-||A|| ||B||= 54-sqrt22 sqrt161$ = -5.514

If A=<−2,3,3>A= <-2 ,3 ,3 > and B=<−9,4,8>B= <-9 ,4 ,8 >, what is A⋅B−||A||||B||A*B -||A|| ||B||?