What is known about Θ, the angle between two nonzero vectors u and v, if each of the following is true? Explain your answers.
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Answer:
The angle between two nonzero vectors u and v is given by
Cos Θ=u*v/║u║║v║
1) If u*v=0, then CosΘ=0
arccos 0=90°
2) If u*v > 0, then CosΘ >0
If (cos Θ > 0, then Θ is less than 90°
3) If u*v < 0, then Cos Θ < 0
If Cos Θ < 0, then Θ is greater than 90°
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