Vectors: Adding, Subtracting, and Scalar Multiplication

In today’s lesson, we explored the basics of vectors, including how to add and subtract vectors, as well as how to multiply a vector by a scalar. These operations are very important in mathematics and physics because they help us describe quantities that have both magnitude and direction. To apply these concepts, we solved a practical problem involving a force vector. The vector F had a magnitude of 20 newtons and made an angle of 30° with the positive x-axis. Our goal was to find the horizontal and vertical components of this vector, known as Fₓ and Fᵧ. Using trigonometry, we broke the vector into components: The horizontal component is found using cosine: Fₓ = 20 cos(30°) = 10√3 newtons The vertical component is found using sine: Fᵧ = 20 sin(30°) = 10 newtons This means the force can be represented in component form as: F = (10√3, 10) Understanding how to resolve a vector into its components allows us to analyze forces and motions more easily, especially when working in coordinate systems. This is a key skill that will be used in many future topics.