What is the angle between <4 , 7 , -4 > <4,7,−4> and < 5 , 2 , 3 > <5,2,3>?

1 Answer
Binayaka C.
Jul 28, 2016

theta=66.64^0θ=66.640

Explanation:

Let vecu =<4,7, -4> and vecv =<5,2,3> ; theta→u=<4,7,−4>and→v=<5,2,3>;θ be the angle between them ; then we know cos theta= (vecu*vecv)/(||vecu||*||vecv||)=((4.5)+(7*2)+(-4*3))/(sqrt(4^2+7^2+(-4)^2)* (sqrt(5^2+2^2+3^2))cosθ=→u⋅→v∣∣∣∣→u∣∣∣∣⋅∣∣∣∣→v∣∣∣∣=(4.5)+(7⋅2)+(−4⋅3)√42+72+(−4)2⋅(√52+22+32) = 22/(sqrt81*sqrt38)=22/(9*sqrt38)=0.3965:. theta=cos^-1(0.3965)=66.64^0[Ans]

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