https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vectors-intro/v/introduction-to-vectors-and-scalars 2022-11-16T04:22:43.7414897Z Intro to vectors and scalars Scalars and vectors are two kinds of quantities that are used in physics and math. Scalars are quantities that only have magnitude (or size), while vectors have both magnitude and direction. Explore some examples of scalars and vectors, including distance, displacement, speed, and velocity. Sal Khan video https://cdn.kastatic.org/googleusercontent/SFXLQFnHWrTVZaa4NzMWWzUXI3ZJ3WmlUO6lpiswGs9XkUr7Z_mQUVR-smC5VDB3BOQJmyi1dsu0qttkt5cAEAyx Intro to vectors and scalars Scalars and vectors are two kinds of quantities that are used in physics and math. Scalars are quantities that only have magnitude (or size), while vectors have both magnitude and direction. Explore some examples of scalars and vectors, including distance, displacement, speed, and velocity. https://cdn.kastatic.org/ka-youtube-converted/ihNZlp7iUHE.mp4/ihNZlp7iUHE.mp4 519 Vectores y escalares https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vectors-intro/v/representing-quantities-with-vectors 2022-10-07T00:22:18.752150461Z Representing quantities with vectors Vectors can represent real-world quantities where it's important to have both a magnitude and a direction. One example for that is force: you want to represent a force's magnitude (or strength), but it's also important to indicate in what direction the force is applied. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/c0bf5064-85dc-4055-aca6-9572f779ed4a_1280_720_base.png Representing quantities with vectors Vectors can represent real-world quantities where it's important to have both a magnitude and a direction. One example for that is force: you want to represent a force's magnitude (or strength), but it's also important to indicate in what direction the force is applied. https://cdn.kastatic.org/ka-youtube-converted/TCOQzIONaz8.mp4/TCOQzIONaz8.mp4 166 Vectores y escalares https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vectors-intro/e/equivalent-vectors 2026-03-10T05:00:40.135420241Z Vectors intro Determine if two vectors shown on a graph are equivalent. Ben Stenhaug exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vectors-intro/v/interpreting-statements-about-vectors 2022-10-07T00:22:18.752150461Z Interpreting statements about vectors Vector quantities have both a magnitude and a direction. In this example, we interpret a mathematical statement about two vector quantities in terms of the real-world quantities they represent. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/256838d5-f2e0-4618-9cd2-f144e455147e_1280_720_base.png Interpreting statements about vectors Vector quantities have both a magnitude and a direction. In this example, we interpret a mathematical statement about two vector quantities in terms of the real-world quantities they represent. https://cdn.kastatic.org/ka-youtube-converted/eA2AW5F4N_M.mp4/eA2AW5F4N_M.mp4 158 Vectores y escalares https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vector-components/v/introduction-to-vector-components 2022-10-07T00:22:18.752150461Z Introduction to vector components Vectors are quantities that have a magnitude and a direction. In the two-dimensional plane, we can describe them in an equivalent way, by thinking about the changes in x and y from the vector's tail to its head. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/817f6e7c-c6d5-4ce1-b85c-7e97e1402f31_1280_720_base.png Introduction to vector components Vectors are quantities that have a magnitude and a direction. In the two-dimensional plane, we can describe them in an equivalent way, by thinking about the changes in x and y from the vector's tail to its head. https://cdn.kastatic.org/ka-youtube-converted/hJkKADcQWj0.mp4/hJkKADcQWj0.mp4 316 Vectores y escalares https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vector-components/v/example-finding-components-of-a-vector 2022-09-27T03:20:10.805796422Z Finding the components of a vector Sal finds the x and y-components of a vector given its graph. video https://cdn.kastatic.org/ka_thumbnails_cache/ccdf9069-d4e1-40c8-8580-2ceb2f92a912_1280_720_base.png Finding the components of a vector Sal finds the x and y-components of a vector given its graph. https://cdn.kastatic.org/ka-youtube-converted/BmDph4uNfPI.mp4/BmDph4uNfPI.mp4 198 Vectores y escalares https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vector-components/v/example-comparing-x-components-of-vectors 2022-09-27T03:20:10.805796422Z Comparing the components of vectors Sal figures out which vectors have the same x-component given the graphs of 4 different vectors. video https://cdn.kastatic.org/ka_thumbnails_cache/f9cce388-46cc-49c8-97f8-0a9d5cb4ba33_1280_720_base.png Comparing the components of vectors Sal figures out which vectors have the same x-component given the graphs of 4 different vectors. https://cdn.kastatic.org/ka-youtube-converted/v7ZZ1ctT1k0.mp4/v7ZZ1ctT1k0.mp4 175 Vectores y escalares https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vector-components/e/components_of_vectors 2026-04-07T23:55:07.30621384Z Components of vectors from endpoints Find the components of a vector given its starting point and end point. Ben Sten exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vec-mag/v/example-calcuating-magnitude-of-vector-from-graph 2021-05-05T14:53:18Z Vector magnitude from graph Sal finds the magnitude of a vector given its graph. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Vector magnitude from graph Sal finds the magnitude of a vector given its graph. https://cdn.kastatic.org/ka-youtube-converted/-U53eHKCLcg.mp4/-U53eHKCLcg.mp4 218 Vectores y escalares https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vec-mag/v/finding-vector-magnitude-from-components 2022-09-27T03:20:10.805796422Z Vector magnitude from components Sal finds the magnitude of a vector given its components of (5, -3). video https://cdn.kastatic.org/ka_thumbnails_cache/5f8adaaa-5a94-438c-825f-f58fda9b1f1f_1280_720_base.png Vector magnitude from components Sal finds the magnitude of a vector given its components of (5, -3). https://cdn.kastatic.org/ka-youtube-converted/qMZnsj4ZO9g.mp4/qMZnsj4ZO9g.mp4 186 Vectores y escalares https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vec-mag/v/vector-magnitude-from-initial-and-terminal-points 2021-05-05T14:53:18Z Vector magnitude from initial & terminal points Example of finding the magnitude of a vector when what we're given about the vector is where it starts and where it ends. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Vector magnitude from initial & terminal points Example of finding the magnitude of a vector when what we're given about the vector is where it starts and where it ends. https://cdn.kastatic.org/ka-youtube-converted/jfaSZhNFEOE.mp4/jfaSZhNFEOE.mp4 323 Vectores y escalares https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vec-mag/e/magnitude-of-vectors 2026-04-07T22:23:57.656416987Z Magnitude of vectors Find the magnitude of a vector. You'll see vectors given in graphs, given in component form, and given by initial and terminal points. Ben Stenhaug exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:scalar-mul/v/understanding-multiplying-vectors-by-scalars 2021-07-29T20:12:07.191455011Z Scalar multiplication: component form Sal explains what happens graphically and to the components of a vector when we multiply it by a scalar. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Scalar multiplication: component form Sal explains what happens graphically and to the components of a vector when we multiply it by a scalar. https://cdn.kastatic.org/ka-youtube-converted/JuTvjQgpUMQ.mp4/JuTvjQgpUMQ.mp4 342 Vectores y escalares https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:scalar-mul/v/examples-from-understanding-scalar-multiplication-exercise 2021-07-29T20:12:07.191455011Z Scalar multiplication: magnitude and direction Sal analyzes the magnitude and direction of vectors that are a result of scalar multiplication of a vector whose magnitude is given. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Scalar multiplication: magnitude and direction Sal analyzes the magnitude and direction of vectors that are a result of scalar multiplication of a vector whose magnitude is given. https://cdn.kastatic.org/ka-youtube-converted/kLLsJXc1E1E.mp4/kLLsJXc1E1E.mp4 293 Vectores y escalares https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:scalar-mul/e/scaling_vectors 2026-03-24T23:41:07.080866137Z Scalar multiplication Practice your understanding of vector scalar multiplication. Tomer Gal exercise