If $A= <2 ,-3 ,9 >$ and $B= <-2 ,5 ,7 >$ , what is $A*B -||A|| ||B||$ ?

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Answer 1 · 2017-01-06T10:21:18

The answer is $=-41.6$

Let's start by calculating the dot product

$vecA.vecB=〈2,-3,9〉.〈-2,5,7〉=-4-15+63=44$

The magnitude of $vecA$ = $∥vecA∥=∥〈2,-3,9〉∥=sqrt(4+9+81)=sqrt94$

The magnitude of $vecB$ = $∥vecB∥=∥〈-2,5,7〉∥=sqrt(4+25+49)=sqrt78$

Therefore,

$vecA.vecB-∥vecA∥*∥vecB∥=44-sqrt94*sqrt78=-41.6$

If A= <2 ,-3 ,9 >A= <2 ,-3 ,9 > and B= <-2 ,5 ,7 >B= <-2 ,5 ,7 >, what is A*B -||A|| ||B||A*B -||A|| ||B||?