If #A = <2 ,4 ,-3 >#, #B = <3 ,4 ,1 ># and #C=A-B#, what is the angle between A and C?

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Answer 1 · 2018-03-24T12:10:21

The angle between #vecA and vecC# is #63.23^0#

#vec C=vecA- vecB = (< 2,4,-3 >) - (< 3,4,1 >)#

#=(< (2-3),(4-4),(-3-1) >) =< -1,0,-4 >#

#vecA =<2,4,-3> and vecC =<-1,0,-4> # Let #theta# be the

angle between them ; then we know

#cos theta= (vecA*vecC)/(||vecA||*||vecC||)#

#=(2* (-1)+(4*0)+(-3*(-4)))/(sqrt(2^2+4^2+(-3)^2)* (sqrt((-1)^2+0^2+(-4)^2))#

#= 10/(sqrt29*sqrt17)=10/22.2 ~~ 0.4504#

#:. theta=cos^-1(0.4504)~~63.23^0#

The angle between #vecA and vecC# is #63.23^0# [Ans]