Category: Rectangular Coordinate System

Example 4: Find a unit vector v with the same direction as the vector u given that u = ⟨7, − 1⟩. Two special unit vectors, i = ⟨1, 0⟩ and j = ⟨0, 1⟩, can be used to express any vector v = ⟨a, b⟩. Example 5: Write u = ⟨5, 3⟩ in terms of the i and j unit vectors (Figure 5 ). Figure 5              Drawing for Example 5.…

Figure 2               Drawing for Example 1. If the coordinates of point P are ( x, y), An algebraic vector is an ordered pair of real numbers. An algebraic vector that corresponds to standard geometric vector  is denoted as ⟨ a, b⟩ if terminal point P has coordinates of (a, b). The numbers a and b are called the components of vector ⟨ a, b⟩ (see Figure…

The following discussion is limited to vectors in a two‐dimensional coordinate plane, although the concepts can be extended to higher dimensions. If vector  is shifted so that its initial point is at the origin of the rectangular coordinate plane, it is said to be in standard position. If vector  is equal to vector  and has its initial point at…