If $A= <-1 ,6 ,-4 >$ and $B= <7 ,2 ,4 >$ , what is $A*B -||A|| ||B||$ ?

Question

1612 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-15T07:10:49

The answer is $=-71.5$

$vecA=〈-1,6,-4〉$

$vecB=〈7,2,4〉$

The dot product is $vecA.vecB=〈-1,6,-4〉.〈7,2,4〉$

$=-7+12-16=-11$

The modulus of $vecA$ is $=∥vecA∥=∥〈-1,6,-4〉∥$

$=sqrt(1+36+16)=sqrt53$

The modulus of $vecB$ is $=∥vecB∥=∥〈7,2,4〉∥$

$=sqrt(49+4+16)=sqrt69$

Therefore,

$vecA.vecB-∥vecA∥*∥vecB∥=-11-sqrt53*sqrt69$

$=-11-60.5=-71.5$

If A= <-1 ,6 ,-4 >A= <-1 ,6 ,-4 > and B= <7 ,2 ,4 >B= <7 ,2 ,4 >, what is A*B -||A|| ||B||A*B -||A|| ||B||?