Question

If `A= <6 ,-4 ,-1 >` and `B= <2 ,-9 ,3 >`, what is `A*B -||A|| ||B||`?

Answer 1

With the given data we start,

`A*B=<6*2,(-4)*(-9),(-1)*3>`

`A*B=<+12,+36,-3>`

`A*B=45`

`||A||=sqrt(6^2+(-4)^2+(-1)^2)`

`||A||=sqrt(36+16+1)`

`||A||=sqrt(53)`

`||A|| ~~7.28`

`||B||=sqrt(2^2+(-9)^2+3^2`

`||B||=sqrt(94)`

`||B|| ~~9.70`

Now lets plug in values

`A*B -||A|| ||B||=45-(7.28)(9.70)`

`A*B -||A|| ||B||=45-70.616`

`A*B -||A|| ||B||=-25.616`