Find the component form of a vector

Learning Objectives Define a vector and its components. Identify the initial and terminal points of a vector from a diagram or description. Calculate the horizontal and vertical components of a vector given its initial and terminal points. Write a vector in its proper component form using angle brackets. Distinguish between the notation for a vector in component form and the notation for a coordinate point. Represent a vector in component form by drawing it in standard position on a coordinate plane. Ever given directions like 'go three blocks east and two blocks north'? 🗺️ You were using the basic idea of a vector's component form! In this tutorial, you will learn how to break down a vector, which has both length and direction, into its simple horizontal and...

TermDefinitionExample VectorA mathematical quantity that has both magnitude (size or length) and direction. It is often represented by an arrow.A car traveling 60 km/h due east can be represented by a vector. Initial PointThe starting point of a vector, often called the 'tail' of the arrow.For a vector representing a trip from City A to City B, City A is the initial point. Terminal PointThe ending point of a vector, often called the 'head' of the arrow.For a vector representing a trip from City A to City B, City B is the terminal point. Component FormA representation of a vector written as <v₁, v₂>, where v₁ is the horizontal component and v₂ is the vertical component.The vector <3, -4> represents a displacement of 3 units to the right and 4 units down. Hor...

Component Form Formula Given an initial point P(x₁, y₁) and a terminal point Q(x₂, y₂), the component form of vector PQ is given by: \vec{PQ} = \langle x_2 - x_1, y_2 - y_1 \rangle Use this formula to find the component form of any vector when you know its starting and ending coordinates. Subtract the initial point's coordinates from the terminal point's coordinates. Identifying Components For a vector \mathbf{v} = \langle v_1, v_2 \rangle: \\ v_1 = \text{horizontal component} \\ v_2 = \text{vertical component} This rule helps you interpret a vector in component form. A positive v₁ means movement to the right; negative means left. A positive v₂ means movement up; negative means down.