If $A= <6 ,9 ,-1 >$ and $B= <9 ,-1 ,8 >$ , what is $A*B -||A|| ||B||$ ?

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Answer 1 · 2016-03-23T10:15:43

$A * B - ||A|| * ||B|| = 37 - sqrt(118)*sqrt(146)$

$A * B$ is a dot product (or scalar product) and can be computed as follows:

$A = < color(blue)(6), color(green)(" "9), color(purple)(-1) >$
$B = < color(blue)(9), color(green)(-1), color(purple)(" "8) >$

$=> " " A * B = color(blue)(6 * 9) + color(green)(9 * (-1)) + color(purple)((-1) * 8) = 37$

$||A||$ and $||B||$ can be computed as follows:

$||A|| = sqrt(6^2 + 9^2 + (-1)^2) = sqrt(36 + 81 + 1) = sqrt(118)$

$||B|| = sqrt(9^2 + (-1)^2 + 8^2) = sqrt(81 + 1 + 64) = sqrt(146)$

In total, you have

$A * B - ||A|| * ||B|| = 37 - sqrt(118)*sqrt(146) ~~94,26$

If A= <6 ,9 ,-1 >A= <6 ,9 ,-1 > and B= <9 ,-1 ,8 >B= <9 ,-1 ,8 >, what is A*B -||A|| ||B||A*B -||A|| ||B||?