Use the figure to find each vector: - u. Use vector notation as in Example 4.


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Key Concepts

Vector Notation

Vector notation is a mathematical representation of vectors, typically denoted as an ordered pair or triplet of numbers that indicate its components along the coordinate axes. For example, a vector u in two dimensions can be represented as u = <x, y>, where x and y are the horizontal and vertical components, respectively. Understanding this notation is essential for accurately describing and manipulating vectors in trigonometry.

Vector Addition

Vector addition is the process of combining two or more vectors to produce a resultant vector. This is done by adding the corresponding components of the vectors. For instance, if vector u = <x1, y1> and vector v = <x2, y2>, their sum is u + v = <x1 + x2, y1 + y2>. Mastery of vector addition is crucial for solving problems involving multiple vectors and understanding their interactions.

Magnitude of a Vector

The magnitude of a vector is a measure of its length and is calculated using the Pythagorean theorem. For a vector u = <x, y>, the magnitude is given by ||u|| = √(x² + y²). This concept is important for understanding the size of a vector in relation to its direction, which is fundamental in trigonometry and physics when analyzing forces and motion.