8.6 Vector Operations

  • Perform calculations with vectors in component form.

  • Express a vector as a linear combination of unit vectors.

  • Express a vector in terms of its magnitude and its direction.

  • Find the angle between two vectors using the dot product.

  • Solve applied problems involving forces in equilibrium.

Position Vectors

Let’s consider a vector v whose initial point is the origin in an xy-coordinate system and whose terminal point is (a, b). We say that the vector is in standard position and refer to it as a position vector. Note that the ordered pair (a, b) defines the vector uniquely. Thus we can use (a, b) to denote the vector. To emphasize that we are thinking of a vector and to avoid the confusion of notation with ordered-pair ...

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