Let θ be the angle between the vectors g and h .
Using the transformed dot product equation,
θ=cos−1(∣g∣∣h∣g⋅h)
where
g⋅h=(1)(0)+(2)(−3)+(−3)(4)=−18 (the dot product of g and h )
and
∣g∣=(1)2+(2)2+(−3)2=14 (magnitude of vector g )
∣h∣=(0)2+(−3)2+(4)2=25=5 (magnitude of vector h )
Therefore,
θ=cos−1(14(5)−18)
θ=cos−1(−0.9621)
θ=164.180
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