Vector Notation and Operations

Trigonometry · Axiom Academy

LESSON Vector Notation and Operations Understanding vectors as quantities with both magnitude and direction, and learning to perform operations on them both geometrically and algebraically. We denote vectors with boldface (like v ) or with an arrow (like ). The magnitude of vector is written as or . Any vector can be broken down into horizontal and vertical components. This is called component form and is written as an ordered pair. The magnitude can be found using the Pythagorean theorem, and the direction angle can be found using inverse tangent: Vectors can be added both geometrically and algebraically. The result is called the resultant vector . Vector subtraction is the same as adding and the opposite of (that is, , which has the same magnitude but opposite direction). Multiplying a vector by a scalar (a number) changes its magnitude but preserves (or reverses) its direction. If k > 1 : vector stretches (same direction, longer) If 0 < k < 1 : vector shrinks (same direction, shorter) If k < 0 : vector reverses direction and scales by |k|

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