vec C=vecA- vecB = (< 2,4,-3 >) - (< 3,4,1 >)→C=→A−→B=(<2,4,−3>)−(<3,4,1>)
=(< (2-3),(4-4),(-3-1) >) =< -1,0,-4 >=(<(2−3),(4−4),(−3−1)>)=<−1,0,−4>
vecA =<2,4,-3> and vecC =<-1,0,-4> →A=<2,4,−3>and→C=<−1,0,−4> Let thetaθ be the
angle between them ; then we know
cos theta= (vecA*vecC)/(||vecA||*||vecC||)cosθ=→A⋅→C∣∣∣∣∣∣→A∣∣∣∣∣∣⋅∣∣∣∣∣∣→C∣∣∣∣∣∣
=(2* (-1)+(4*0)+(-3*(-4)))/(sqrt(2^2+4^2+(-3)^2)* (sqrt((-1)^2+0^2+(-4)^2))=2⋅(−1)+(4⋅0)+(−3⋅(−4))√22+42+(−3)2⋅(√(−1)2+02+(−4)2)
= 10/(sqrt29*sqrt17)=10/22.2 ~~ 0.4504=10√29⋅√17=1022.2≈0.4504
:. theta=cos^-1(0.4504)~~63.23^0
The angle between vecA and vecC is 63.23^0 [Ans]
