Welcome to physics vectors! A vector is a fundamental concept in physics that represents a quantity with both magnitude and direction. Unlike scalars which only have size, vectors tell us not just how much, but also which way. Common examples include displacement, velocity, and force.
Vectors can be represented in two main ways. Graphically, we draw them as arrows where the length represents magnitude and the direction shows the vector's direction. Mathematically, we use components. For example, this vector has x-component 4 and y-component 3, written as v equals 4, 3. The magnitude is calculated using the Pythagorean theorem, giving us 5 units.
Vector addition combines two or more vectors to find a resultant vector. The tip-to-tail method places the tail of the second vector at the tip of the first, and the resultant goes from the starting point to the final tip. Alternatively, we can add components: A plus B equals the sum of their x-components and y-components. For example, 3,2 plus 1,3 equals 4,5.
Vector subtraction is performed by adding the negative of the second vector. A minus B equals A plus negative B. Scalar multiplication changes a vector's magnitude and possibly its direction. Multiplying by a scalar greater than one increases magnitude, while multiplying by a value between zero and one decreases it. Negative scalars reverse the vector's direction.
To summarize what we've learned about physics vectors: Vectors are quantities with both magnitude and direction, unlike scalars which only have magnitude. They can be represented as arrows or using mathematical components. Vector addition combines vectors using the tip-to-tail method or by adding components. Scalar multiplication scales vectors and can reverse their direction. Understanding vectors is essential for describing motion, forces, and fields throughout physics.