# If #A= <5 ,1 ,-2 ># and #B= <4 ,-2 ,3 >#, what is #A*B -||A|| ||B||#?

##### 1 Answer

May 12, 2017

#### Explanation:

For two vectors

For

#A*B=(5*4)+(1*-2)+(-2*3)=20-2-6=color(blue)12#

The next part is the product of the magnitudes of vectors

#|A|=sqrt((A_x)^2+(A_y)^2+(A_z)^2 )#

For the given vectors

#|A|=sqrt((5)^2+(1)^2+(-2)^2)=sqrt(25+1+4)=sqrt(30)#

#|B|=sqrt((4)^2+(-2)^2+(3)^2)=sqrt(16+4+9)=sqrt(29)#

We then have

Then