If $A= <-5 ,3 ,-3 >$ and $B= <2 ,2 ,8 >$ , what is $A*B -||A|| ||B||$ ?

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Answer 1 · 2016-12-28T02:46:11

$A*B-||A||||B|| = -28-6sqrt(86)~~-83.64$

Given vectors $vec(x) = <x_1, x_2, x_3>$ and $vec(y) = <y_1, y_2, y_3>$ , we have

$vec(x)*vec(y) = x_1y_1+x_2y_2+x_3y_3$

and

$||vec(x)|| = sqrt(x_1^2+x_2^2+x_3^2)$

Using these on the given vectors, we have

$A*B = -5(2)+3(2)+(-3)(8) = -10+6-24 = -28$

and

$||A||||B|| = sqrt((-5)^2+3^2+(-3)^2)*sqrt(2^2+2^2+8^2)$

$=sqrt(43)*sqrt(72)$

$=6sqrt(86)$

so, taken together

$A*B-||A||||B|| = -28-6sqrt(86)~~-83.64$

If A= <-5 ,3 ,-3 >A= <-5 ,3 ,-3 > and B= <2 ,2 ,8 >B= <2 ,2 ,8 >, what is A*B -||A|| ||B||A*B -||A|| ||B||?