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 xycoordinate 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 orderedpair ...
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