https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/intro-unit-vector-notation 2021-04-11T10:35:11Z Unit vectors intro Unit vectors are vectors whose magnitude is exactly 1 unit. They are very useful for different reasons. Specifically, the unit vectors [0,1] and [1,0] can form together any other vector. Sal Khan video https://cdn.kastatic.org/googleusercontent/j0_ggT8J2YR7i8ZN8xZMoAoEGyOK0mTfgEIlrigp-RVPZQGdk3p4hSNKYvi4dPRcL9pwQI2Tqqg9S2Skz7D-fDmGXg Unit vectors intro Unit vectors are vectors whose magnitude is exactly 1 unit. They are very useful for different reasons. Specifically, the unit vectors [0,1] and [1,0] can form together any other vector. https://cdn.kastatic.org/ka-youtube-converted/9ylUcCOTH8Y.mp4/9ylUcCOTH8Y.mp4 479 Multiplication of vector by a scalar https://www.khanacademy.org/science/in-in-class11th-physics/in-in-class11th-physics-motion-in-a-plane/in-in-phy-review-unit-vectors/v/unit-vector-notation-part-2 2021-02-07T17:14:01Z Unit vector notation (part 2) More on unit vector notation. Showing that adding the x and y components of two vectors is equivalent to adding the vectors visually using the head-to-tail method Sal Khan video https://cdn.kastatic.org/googleusercontent/GXK8YkCkokkkd0mK3Hy6HsCnn9KOy1U_67BX8wqtVHt-YNWLGEMwDLgXuUCAtSXF8Fx9DABS1QZ7v4kIMZ7lmNMLwA Unit vector notation (part 2) More on unit vector notation. Showing that adding the x and y components of two vectors is equivalent to adding the vectors visually using the head-to-tail method https://cdn.kastatic.org/ka-youtube-converted/595Tiga1gIg.mp4/595Tiga1gIg.mp4 553 Multiplication of vector by a scalar https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/e/unit-vector 2025-03-12T14:20:10.072734823Z Unit vectors Find a unit vector in the direction of a given vector. Rhonda Hughes exercise https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/multiplying-vector-by-scalar 2020-07-15T21:04:49Z Multiplying a vector by a scalar Watch Sal change the magnitude of a vector by multiplying it by a scalar. Sal Khan video https://cdn.kastatic.org/googleusercontent/DV9R8ilNd_ZRJ9SWdNtBlQa0hjAAZcanm8y6v4upGDLsFsnyUNwiYQv2m_qhKRvh90nM4rW8CRMOm4T9LVRHhCsQFA Multiplying a vector by a scalar Watch Sal change the magnitude of a vector by multiplying it by a scalar. https://cdn.kastatic.org/ka-youtube-converted/ZN7YaSbY3-w.mp4/ZN7YaSbY3-w.mp4 344 Multiplication of vector by a scalar 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 Multiplication of vector by a scalar 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 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 Multiplication of vector by a scalar https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:vector-algebra-ncert-new/x6f66cbee9a2f805b:multiplication-of-vector-by-a-scalar/v/finding-vector-given-direction-and-magnitude 2025-05-22T13:12:03.767544849Z Finding vector given direction and magnitude In this video, we use the information given about the vector - its magnitude and direction, to write it in its component form. We also learn how to find unit vectors along given vectors. Finally, we find unit vector using the direction angles made by it with the axes. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Finding vector given direction and magnitude In this video, we use the information given about the vector - its magnitude and direction, to write it in its component form. We also learn how to find unit vectors along given vectors. Finally, we find unit vector using the direction angles made by it with the axes. https://cdn.kastatic.org/ka-youtube-converted/NnOsuGRYqnM.mp4/NnOsuGRYqnM.mp4 464 Multiplication of vector by a scalar https://www.khanacademy.org/science/in-in-class11th-physics/in-in-class11th-physics-vectors-prerequisite/in-in-class11th-physics-vectors-prerequisite-component-form-of-vectors/e/addition-subtraction-and-scalar-multiplication-in-unit-vector-notation 2025-03-12T14:20:10.072734823Z Addition, subtraction and scalar multiplication in unit vector notation Let's solve some problems to better understand addition, subtraction, and scalar multiplication in unit vector notation. Aakash Bagga exercise 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/ka-math-class-12/x6f66cbee9a2f805b:vector-algebra-ncert-new/x6f66cbee9a2f805b:multiplication-of-vector-by-a-scalar/v/collinearity-in-3d 2025-05-22T13:12:03.767544849Z Collinearity in 3D In this video, we talk about collinearity in 3D. We first refresh what collinear vectors are. We then figure out what it takes for the components (or direction ratios) to make the vectors collinear. We then solve a problem applying the result. We then uncover what it takes for three points to be collinear. There are two methods for this one. Either prove that two vectors are collinear. Or prove that these three points can't form a triangle in space - which means that sum of side lengths (or magnitude) of two vectors is equal to the third. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Collinearity in 3D In this video, we talk about collinearity in 3D. We first refresh what collinear vectors are. We then figure out what it takes for the components (or direction ratios) to make the vectors collinear. We then solve a problem applying the result. We then uncover what it takes for three points to be collinear. There are two methods for this one. Either prove that two vectors are collinear. Or prove that these three points can't form a triangle in space - which means that sum of side lengths (or magnitude) of two vectors is equal to the third. https://cdn.kastatic.org/ka-youtube-converted/Z3aW1hbXofA.mp4/Z3aW1hbXofA.mp4 484 Multiplication of vector by a scalar https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:vector-algebra-ncert-new/x6f66cbee9a2f805b:multiplication-of-vector-by-a-scalar/e/collinearity-of-vectors 2025-08-08T02:45:51.78671331Z Collinearity of vectors Collinearity of vectors Ashish Gupta exercise