If $A= <2 ,6 ,-3 >$ and $B= <-6 ,4 ,7 >$ , what is $A*B -||A|| ||B||$ ?

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Answer 1 · 2016-05-06T10:53:02

$-9-7sqrt(101)$

This question is vector types.
First, using dot-product since $A.B$

Given $A=<2,6,-3>$ and $B=<-6,4,7>$

then,

$A.B$ = $<2,6,-3>$ . $<-6,4,7>$
$A.B$ = $(2)(-6)+(6)(4)+(-3)(7)$
$A.B$ = $-9$

For $||A|| &||B||$ use, $sqrt(a^2+b^2+c^2)$ where $a,b,c$ are coefficient of vector.

$||A||$ = $sqrt(2^2+6^2+(-3)^2)$ = $7$
and
$||B||$ = $sqrt((-6)^2+4^2+7^2)$ = $sqrt(101)$
Since $||A|| . ||B||$ = $7sqrt(101)$

$A.B- ||A|| . ||B||$ = $-9-7sqrt(101)$

If A= <2 ,6 ,-3 >A= <2 ,6 ,-3 > and B= <-6 ,4 ,7 >B= <-6 ,4 ,7 >, what is A*B -||A|| ||B||A*B -||A|| ||B||?