25.7: Sample problems and solutions
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a. The displacement vector is given by:
→d=(456)−(123)=(333)
b. We can find the angle that this vector makes with the x axis by taking the scalar product of the displacement vector and the unit vector in the x direction (1,0,0):
ˆx⋅→d=(1)(3)+(0)(3)+(0)(3)=3
This is equal to the product of the magnitude of ˆx and →d multiplied by the cosine of the angle between them:
ˆx⋅→d=||ˆx||||→d||cosθ=(1)(√32+32+32)cosθ=√27cosθ3=√27cosθ∴