--- title: "Resolving Vectors into Components" description: "Splitting one vector into two perpendicular parts with sine and cosine, then adding several vectors by adding their components. Scale drawing gives way to a method that stays exact however many forces" canonical: https://lightmysky.com/learn/science/resolving-vectors-into-components-mt_tc698unGJG source: https://lightmysky.com/learn/science/resolving-vectors-into-components-mt_tc698unGJG.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Resolving Vectors into Components Splitting one vector into two perpendicular parts with sine and cosine, then adding several vectors by adding their components. Scale drawing gives way to a method that stays exact however many forces act. Subject: Science · Area: Forces & Motion · Ages 16 to 17 Page: https://lightmysky.com/learn/science/resolving-vectors-into-components-mt_tc698unGJG ## Ready when they can - Resolves a force or a velocity into components along any chosen pair of perpendicular axes - Adds three or more coplanar vectors by components and states the resultant as a size and an angle - Picks the axes that make a problem shortest and says why that choice is free ## Lesson: Resolving vectors into parts A kicked ball flies sideways and upward from a single push. Resolving splits that one vector into perpendicular parts, usually horizontal and vertical, where each part acts alone along its axis. From size A and angle from the x axis, the x part is A times cos and the y part is A times sin, since cosine sits beside the angle. A velocity of 20 metres per second at 30 degrees gives 20 times 0.5, which is 10 upward, and about 17.3 sideways. Adding vectors by components is bookkeeping: add all x parts for the total x, add all y parts for the total y, then size and angle come from Pythagoras and tan. Three pulls on a ring with x parts 4, 2 and 2 add to 8, and y parts 1, 2 and 3 add to 6, so the resultant is 10 at about 37 degrees above east. **Example.** Pick the axes that kill the most terms: align one axis with the motion or the slope to shorten the maths. On a slope of angle theta, weight splits into m g sin theta down the slope and m g cos theta into it. Tilt swaps which trig sits where, so always sketch the triangle before you write. The axes are your measuring choice: turning them changes the numbers but not the motion itself. **Tip.** You may point the axes anywhere: the physics is unchanged, only the arithmetic gets easier or harder. If your angle is measured from the y axis instead, sine and cosine swap sides. **Recap.** Split each vector with cos beside the angle, add part by part, and choose axes that kill terms. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Vectors, Scalars and Free-Body Diagrams](https://lightmysky.com/learn/science/vectors-scalars-and-free-body-diagrams-mt_erzORFj2-1) - [Trigonometry basics](https://lightmysky.com/learn/mathematics/trigonometry-basics-mt_KB_Czd7RQH) ## Opens up - [Projectile Motion as Two Independent Motions](https://lightmysky.com/learn/science/projectile-motion-as-two-independent-motions-mt_OBgL97RFbb) - [Newton's Second Law on a Slope](https://lightmysky.com/learn/science/newtons-second-law-on-a-slope-mt_OR_sKFelnP) - [Velocity and Acceleration as Derivatives](https://lightmysky.com/learn/science/velocity-and-acceleration-as-derivatives-mt_RdhbiJ6CTk)