# If #A = <4 ,-5 ,-4 >#, #B = <-9 ,1 ,-6 ># and #C=A-B#, what is the angle between A and C?

##### 1 Answer

#### Explanation:

If

and

then

#A*C= color(blue)(4)xxcolor(red)(13) +color(blue)((-5))xxcolor(red)((-6))+color(blue)((-4))xxcolor(red)(2)#

#color(white)("XXX")= 76#

#||A|| = sqrt(color(blue)(4)^2+color(blue)((-5))^2+color(blue)((-4))^2)#

#color(white)("XXX")=sqrt(57)#

#||C|| =sqrt(color(red)(13)^2+color(red)((-6))^2+color(red)(2)^2)#

#color(white)("XXX")=sqrt(209)#