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Vector fields, introduction

Khan AcademyGrant Sanderson

Vector fields, introduction

Vector fields let you visualize a function with a two-dimensional input and a two-dimensional output. You end up with, well, a field of vectors sitting at various points in two-dimensional space.

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Vector Field Visualization

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How can we visualize forces like gravity? Vector fields make it possible by assigning an arrow to ev

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179K views · 945 reactions | A vector field is a mathematical...

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A vector field assigns a vector to every point in a region of space, allowing us to visualize how a quantity changes from place to place. Each vector has both a direction and a magnitude, so a vector field captures not just the presence of a phenomenon but also how it flows, rotates, or expands. You can think of it like a map of tiny arrows: at every point, the arrow tells you “which way” and “how strongly” something is acting. In physics, these arrows might represent gravitational pull, electri

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A vector field assigns a vector to every point in a region of space, allowing us to visualize how a quantity changes from place to place. Each vector has both a direction and a magnitude, so a vector field captures not just the presence of a phenomenon but also how it flows, rotates, or expands. You can think of it like a map of tiny arrows: at every point, the arrow tells you “which way” and “how strongly” something is acting. In physics, these arrows might represent gravitational pull, electri

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mathswithmuza on Instagram: "A vector field is a mathematical construct that assigns a vector to every point in a given region of space. In two dimensions, you can picture this as arrows drawn on the plane, where each arrow has both a direction and a magnitude that vary depending on the point’s location. In three dimensions, vector fields are often used to describe forces such as gravity, electric fields, or fluid flow, where at each point in space the field indicates the direction and strength

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