https://www.khanacademy.org/math/cambridge-o-level-mathematics-4024/x3f4c73d082a798eb:transformations-and-vectors/x3f4c73d082a798eb:vector-geometry/v/magnitude-and-direction-of-position-vectors-in-3d 2025-05-22T13:12:03.767544849Z Magnitude and direction of position vectors in 3D In this video, we look at ways to find the magnitude and direction of position vectors. We derive the formula for the magnitude of a position vector. We look at a few lazy ways to talk about direction of a vector before talking about the direction cosines. We also discuss why cosines are better at this than sine or tan. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Magnitude and direction of position vectors in 3D In this video, we look at ways to find the magnitude and direction of position vectors. We derive the formula for the magnitude of a position vector. We look at a few lazy ways to talk about direction of a vector before talking about the direction cosines. We also discuss why cosines are better at this than sine or tan. https://cdn.kastatic.org/ka-youtube-converted/Wxc8bcYpCl8.mp4/Wxc8bcYpCl8.mp4 574 Vector geometry https://www.khanacademy.org/math/algebra-home/alg-vectors/alg-magnitude-direction/a/vector-forms-review 2021-04-29T07:53:44Z Vector forms review Review all the different ways in which we can represent vectors: components, magnitude & direction, and unit vectors. article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:magnitude-direction/v/angles-of-vectors-from-components 2022-09-27T03:20:10.805796422Z Direction of vectors from components: 1st & 2nd quadrants Sal first finds the direction angle of a vector in the first quadrant, then moves onto a trickier one in the second quadrant. video https://cdn.kastatic.org/ka_thumbnails_cache/c9c89f5c-3bc1-4c4a-8712-16e7114994a1_1280_720_base.png Direction of vectors from components: 1st & 2nd quadrants Sal first finds the direction angle of a vector in the first quadrant, then moves onto a trickier one in the second quadrant. https://cdn.kastatic.org/ka-youtube-converted/A3OuFLHum6w.mp4/A3OuFLHum6w.mp4 541 Vector geometry https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:component-form/a/vector-magnitude-and-direction-review 2024-10-28T20:22:05.023706061Z Converting between vector components and magnitude & direction review Review how to find a vector's magnitude and direction from its components and vice versa. article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:magnitude-direction/e/direction-angles 2024-10-28T20:22:05.023706061Z Direction of vectors Find the direction angle of a vector. Ben Stenhaug exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:magnitude-direction/v/more-examples-finding-vector-angles 2022-09-27T03:20:10.805796422Z Direction of vectors from components: 3rd & 4th quadrants Sal finds the direction angle of a vector in the third quadrant and a vector in the fourth quadrant. video https://cdn.kastatic.org/ka_thumbnails_cache/c13d07bf-97d8-41ca-a686-60b85fcf9fcc_1280_720_base.png Direction of vectors from components: 3rd & 4th quadrants Sal finds the direction angle of a vector in the third quadrant and a vector in the fourth quadrant. https://cdn.kastatic.org/ka-youtube-converted/EX0Ha42WQ24.mp4/EX0Ha42WQ24.mp4 402 Vector geometry https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vector-add-sub/v/subtracting-vectors-with-parallelogram-rule 2022-10-07T00:22:18.752150461Z Subtracting vectors with parallelogram rule The parallelogram rule says that if we place two vectors so they have the same initial point, and then complete the vectors into a parallelogram, then the sum of the vectors is the directed diagonal that starts at the same point as the vectors. To subtract two vectors, we simply add the first vector and the opposite of the second vector, i.e., a+b=a+(-b). Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/7903599e-b788-48e3-954b-40540a3bae92_1280_720_base.png Subtracting vectors with parallelogram rule The parallelogram rule says that if we place two vectors so they have the same initial point, and then complete the vectors into a parallelogram, then the sum of the vectors is the directed diagonal that starts at the same point as the vectors. To subtract two vectors, we simply add the first vector and the opposite of the second vector, i.e., a+b=a+(-b). https://cdn.kastatic.org/ka-youtube-converted/4mRDJf6tShs.mp4/4mRDJf6tShs.mp4 166 Vector geometry https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:vector-add-sub/v/parallelogram-rule-for-vector-addition 2022-10-07T00:22:18.752150461Z Parallelogram rule for vector addition The parallelogram rule says that if we place two vectors so they have the same initial point, and then complete the vectors into a parallelogram, then the sum of the vectors is the directed diagonal that starts at the same point as the vectors. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/88e49511-3fdd-4587-95b5-265ce5c45184_1280_720_base.png Parallelogram rule for vector addition The parallelogram rule says that if we place two vectors so they have the same initial point, and then complete the vectors into a parallelogram, then the sum of the vectors is the directed diagonal that starts at the same point as the vectors. https://cdn.kastatic.org/ka-youtube-converted/Mep0foZMOCg.mp4/Mep0foZMOCg.mp4 140 Vector geometry