vec C=vec A- vec B = (< 2,4,-7 >) - (< 3,5,2 >)→C=→A−→B=(<2,4,−7>)−(<3,5,2>)
=(< 2-3,4-5,-7-2 >) =< -1,-1,-9 >=(<2−3,4−5,−7−2>)=<−1,−1,−9>
vec A =<2,4, -7> and vec C =<-1,-1,-9> ; theta→A=<2,4,−7>and→C=<−1,−1,−9>;θ
be the angle between them ; then we know
cos theta= (vec A*vec C)/(||vec A||*||vec C||)cosθ=→A⋅→C∣∣∣∣∣∣→A∣∣∣∣∣∣⋅∣∣∣∣∣∣→C∣∣∣∣∣∣
=((2* -1)+(4* -1)+(-7* -9))/(sqrt(2^2+4^2+(-7)^2)* (sqrt((-1)^2+(-1)^2+(-9)^2))=(2⋅−1)+(4⋅−1)+(−7⋅−9)√22+42+(−7)2⋅(√(−1)2+(−1)2+(−9)2)
= 57/(sqrt69*sqrt83)=57/75.68. ~~0.7532=57√69⋅√83=5775.68.≈0.7532
:. theta=cos^-1(0.7532)~~41.13^0
The angle between vec A and vec C is 41.13^0 [Ans]
