8.5 Vectors and Applications

  • Determine whether two vectors are equivalent.

  • Find the sum, or resultant, of two vectors.

  • Resolve a vector into its horizontal component and its vertical component.

  • Solve applied problems involving vectors.

We measure some quantities using only their magnitudes. For example, we describe time, length, and mass using units like seconds, feet, and kilograms, respectively. However, to measure quantities like displacement, velocity, or force, we need to describe a magnitude and a direction. Together, magnitude and direction describe a vector. The following are some examples.


An object moves a certain distance in a certain direction.

  • A surveyor steps 20 yd to the northeast.

  • A hiker follows a trail ...

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