Question

If `A= <8 ,-5 ,6 >` and `B= <7 ,1 ,3 >`, what is `A*B -||A|| ||B||`?

Answer 1

The answer is `=16.8`

Explanation:

The dot product is

`vecA.vecB= <8,-5,6>.<7,1,3>=56-5+18=69`

The modulus of `vecA` is

`||vecA||=||<8,-5,6||=sqrt(64+25+36)=sqrt125`

The modulus of `vecB` is

`||vecB||=||<7,1,3||=sqrt(49+1+9)=sqrt59`

Therefore,

`vecA.vecB-||vecA||||vecB||`

`=69-sqrt125sqrt59`

`=-16.8`