Algebra and Trigonometry, 5th Edition

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 ...