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Physics LibreTexts

25.7: Sample problems and solutions

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Exercise 25.7.1
  1. What is the displacement vector from position (1,2,3) to position (4,5,6)?
  2. What angle does that displacement vector make with the x axis?
Answer

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):

ˆxd=(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:

ˆxd=||ˆx||||d||cosθ=(1)(32+32+32)cosθ=27cosθ3=27cosθ


This page titled 25.7: Sample problems and solutions is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Ryan D. Martin, Emma Neary, Joshua Rinaldo, and Olivia Woodman via source content that was edited to the style and standards of the LibreTexts platform.

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