If A = <4 ,-9 ,2 >A=<4,−9,2>, B = <1 ,1 ,-4 >B=<1,1,−4> and C=A-BC=A−B, what is the angle between A and C?

1 Answer
Binayaka C.
Apr 13, 2017

The angle between vec A and vecC →Aand→C is 19.60^019.600

Explanation:

Let vecA =<4, -9, 2>, vecB =<1,1,-4 > , vecC= vec A-vecB = < 3 , -10 , 6>→A=<4,−9,2>,→B=<1,1,−4>,→C=→A−→B=<3,−10,6> ;

Let theta θ be the angle between vec A and vecC→Aand→C ; then we know cos theta= (vecA*vecC)/(||vecA||*||vecC||)cosθ=→A⋅→C∣∣∣∣∣∣→A∣∣∣∣∣∣⋅∣∣∣∣∣∣→C∣∣∣∣∣∣

=((4*3)+(-9*-10)+(2*6))/(sqrt(4^2+(-9)^2+2^2)* (sqrt(3^2+(-10)^2+6^2))=(4⋅3)+(−9⋅−10)+(2⋅6)√42+(−9)2+22⋅(√32+(−10)2+62) = 114/(sqrt101*sqrt145)=0.94202:. theta=cos^-1(0.94202) ~~19.60^0[Ans]

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