Add and subtract vectors

Learning Objectives Define a vector and identify its components. Represent vector addition and subtraction graphically using the head-to-tail method. Add vectors algebraically by adding their corresponding components. Subtract vectors algebraically by subtracting their corresponding components. By the end of of this lesson, students will be able to calculate the resultant vector from the sum or difference of two vectors. Interpret the meaning of a negative vector and the zero vector. Solve simple real-world problems involving the addition or subtraction of vectors. Imagine a plane flying north, but a strong wind is blowing east. Where does the plane actually go? ✈️ Vector math gives us the answer! This tutorial will introduce you to vectors, which are quantities with both...

TermDefinitionExample VectorA mathematical quantity that has both magnitude (size or length) and direction. It is often represented by an arrow.A velocity of 30 km/h North is a vector. We can write it in component form as <0, 30>. ScalarA quantity that has only magnitude, but no direction.A speed of 30 km/h is a scalar. It tells you how fast, but not in which direction. Component FormA way of writing a vector using its horizontal (x) and vertical (y) components, enclosed in angle brackets.The vector **v** = <4, -2> represents a displacement of 4 units to the right and 2 units down. Resultant VectorThe single vector that is the sum or result of adding two or more vectors. It represents the overall effect of the combined vectors.If you walk 3 blocks East and then 4 blocks North,...

Vector Addition (Component Form) If **u** = <u_x, u_y> and **v** = <v_x, v_y>, then **u** + **v** = <u_x + v_x, u_y + v_y> To add two vectors algebraically, simply add their corresponding x-components together and their corresponding y-components together. Vector Subtraction (Component Form) If **u** = <u_x, u_y> and **v** = <v_x, v_y>, then **u** - **v** = <u_x - v_x, u_y - v_y> To subtract one vector from another, subtract the corresponding components. This is equivalent to adding the negative of the second vector: **u** + (-**v**). Head-to-Tail Rule (Graphical Addition) Draw the first vector. Then, draw the second vector starting from the head (arrow tip) of the first vector. The resultant vector is drawn from the tail (start) of...