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

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Answer 1 · 2018-08-07T19:01:32

$A \cdot B - | | A | | | | B | | \approx - 16.15$ $A*B-||A||||B|| ~~ -16.15$

Here,

$A = < 3, 1, - 2 > and B = < 4, - 2, 3 >$ $A=<3,1,-2> and B= <4,-2,3>$

Now , $A \cdot B = < 3, 1, - 2 > \cdot < 4, - 2, 3$ $A*B=<3,1,-2> * <4,-2,3$

$\Rightarrow A \cdot B = (3) (4) + (1) (- 2) + (- 2) (3) = 12 - 2 - 6 = 4$ $=>A*B=(3)(4)+(1)(-2)+(-2)(3)=12-2-6=4$

$| | A | | = \sqrt{{(3)}^{2} + {(1)}^{2} + {(- 2)}^{2}} = \sqrt{9 + 1 + 4} = \sqrt{14}$ $||A||=sqrt((3)^2+(1)^2+(-2)^2)=sqrt(9+1+4)=sqrt14$

$| | B | | = \sqrt{{(4)}^{2} + {(- 2)}^{2} + {(3)}^{2}} = \sqrt{16 + 4 + 9} = \sqrt{29}$ $||B||=sqrt((4)^2+(-2)^2+(3)^2)=sqrt(16+4+9)=sqrt29$

So ,

$A \cdot B - | | A | | | | B | | = 4 - \sqrt{14} \sqrt{29} = 4 - \sqrt{406}$ $A*B-||A||||B||=4-sqrt14sqrt29=4-sqrt406$

$:.A*B-||A||||B|| ~~ -16.15$

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