https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:vector-algebra-ncert-new/x7ce8ca9c5869750b:cross-product-of-vectors-1/v/cross-product-of-unit-vectors 2025-06-25T04:37:22.958747522Z मात्रक सदिशों का सदिश गुणनफल In this video, we familiarise ourselves with the formula for cross product of vectors. We look at a few scenarios and special cases. We then look at cross products of unit vectors along the axes. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw मात्रक सदिशों का सदिश गुणनफल In this video, we familiarise ourselves with the formula for cross product of vectors. We look at a few scenarios and special cases. We then look at cross products of unit vectors along the axes. https://cdn.kastatic.org/ka-youtube-converted/mJU7Hk3tvgk.mp4/mJU7Hk3tvgk.mp4 366 सदिशों का सदिश गुणन (Cross product) https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:vector-algebra-ncert-new/x7ce8ca9c5869750b:cross-product-of-vectors-1/v/cross-product-in-component-form 2025-06-25T04:37:22.958747522Z घटक रूप में सदिश गुणनफल In this video, we learn how to take cross product of two vectors which are given in component form. We first find the cross product using the determinant formula and then understand where the determinant formula comes from. We then also figure out why the distributive property of cross product makes sense using determinants. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw घटक रूप में सदिश गुणनफल In this video, we learn how to take cross product of two vectors which are given in component form. We first find the cross product using the determinant formula and then understand where the determinant formula comes from. We then also figure out why the distributive property of cross product makes sense using determinants. https://cdn.kastatic.org/ka-youtube-converted/_iXVFgqiw2A.mp4/_iXVFgqiw2A.mp4 315 सदिशों का सदिश गुणन (Cross product) https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:vector-algebra-ncert-new/x7ce8ca9c5869750b:cross-product-of-vectors-1/v/finding-perpendicular-vectors-using-cross-product 2025-06-25T04:37:22.958747522Z सदिश गुणनफल के उपयोग से लंबवत् सदिश ज्ञात करना In this video we try to find vectors perpendicular to a pair of given vectors. Since cross products give exactly this, we take the cross product of given vectors. Additionally, if we want to find the unit vectors, we divide the cross product by its magnitude. We also solve a problem where the dot product of the perpendicular is given and we have to find the missing vector. Note - in general, there are two vectors perpendicular to two given vectors - both opposite of each other. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw सदिश गुणनफल के उपयोग से लंबवत् सदिश ज्ञात करना In this video we try to find vectors perpendicular to a pair of given vectors. Since cross products give exactly this, we take the cross product of given vectors. Additionally, if we want to find the unit vectors, we divide the cross product by its magnitude. We also solve a problem where the dot product of the perpendicular is given and we have to find the missing vector. Note - in general, there are two vectors perpendicular to two given vectors - both opposite of each other. https://cdn.kastatic.org/ka-youtube-converted/GfX8SyV68JE.mp4/GfX8SyV68JE.mp4 500 सदिशों का सदिश गुणन (Cross product) https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:vector-algebra-ncert-new/x7ce8ca9c5869750b:cross-product-of-vectors-1/v/finding-area-using-cross-product 2025-06-25T04:37:22.958747522Z सदिश गुणनफल के उपयोग से क्षेत्रफल ज्ञात करना In this video, we derive the formula for the area of a parallelogram using the cross product. We then solve problems where we use the formula to find the area of a triangle, a parallelogram, and a rectangle. In all these problems (except the last one), we first find the vectors representing the adjacent sides, then find their cross product, and then take its magnitude to get to the area. For the last one, we leverage our visualization skills. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw सदिश गुणनफल के उपयोग से क्षेत्रफल ज्ञात करना In this video, we derive the formula for the area of a parallelogram using the cross product. We then solve problems where we use the formula to find the area of a triangle, a parallelogram, and a rectangle. In all these problems (except the last one), we first find the vectors representing the adjacent sides, then find their cross product, and then take its magnitude to get to the area. For the last one, we leverage our visualization skills. https://cdn.kastatic.org/ka-youtube-converted/OM4lLxM0W2Q.mp4/OM4lLxM0W2Q.mp4 420 सदिशों का सदिश गुणन (Cross product) https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:vector-algebra-ncert-new/x7ce8ca9c5869750b:cross-product-of-vectors-1/v/conceptual-questions-on-product-of-vectors 2025-06-25T04:37:22.958747522Z सदिशों के गुणनफल पर संकल्पनात्मक प्रश्न In this video, we test our fundamentals on dot and cross product by answering some conceptual questions. Some examples of the questions discussed in this video include: If one vector is zero, what can we say about the other vector? Are vectors zero when dot product is zero? Are vectors zero when cross product is zero? When are both the products equal? Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw सदिशों के गुणनफल पर संकल्पनात्मक प्रश्न In this video, we test our fundamentals on dot and cross product by answering some conceptual questions. Some examples of the questions discussed in this video include: If one vector is zero, what can we say about the other vector? Are vectors zero when dot product is zero? Are vectors zero when cross product is zero? When are both the products equal? https://cdn.kastatic.org/ka-youtube-converted/WabsIG5ud14.mp4/WabsIG5ud14.mp4 572 सदिशों का सदिश गुणन (Cross product) https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:vector-algebra-ncert-new/x7ce8ca9c5869750b:cross-product-of-vectors-1/v/manipulating-equations-involving-products-of-vectors 2025-06-25T04:37:22.958747522Z सदिशों के गुणनफलों से संबंधित समीकरणों में फेर-बदल करना In this video, we solve problems that apply dot product of vectors. In the first problem, we're given information about the magnitudes of the vectors and their perpendicularity. We're asked to find the magnitude of sum of these vectors. In the second problem, we're given the sum and we're trying to find the sum of pairwise products. In the final problem, we're given two vectors and we're asked to break the second one into two parts - one perpendicular and the other parallel to the first one. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw सदिशों के गुणनफलों से संबंधित समीकरणों में फेर-बदल करना In this video, we solve problems that apply dot product of vectors. In the first problem, we're given information about the magnitudes of the vectors and their perpendicularity. We're asked to find the magnitude of sum of these vectors. In the second problem, we're given the sum and we're trying to find the sum of pairwise products. In the final problem, we're given two vectors and we're asked to break the second one into two parts - one perpendicular and the other parallel to the first one. https://cdn.kastatic.org/ka-youtube-converted/Hop_Fkl1QHk.mp4/Hop_Fkl1QHk.mp4 490 सदिशों का सदिश गुणन (Cross product) https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:vector-algebra-ncert-new/x7ce8ca9c5869750b:cross-product-of-vectors-1/v/linear-algebra-cross-product-introduction 2020-08-13T10:51:20Z सदिश गुणनफल का परिचय (Cross product Introduction) सदिश गुणनफल का परिचय Sal Khan video https://cdn.kastatic.org/googleusercontent/P6fTzoK6rLVVQF4eua0JeaGV21oApezgfDFJUpaeJfx83aMRo1KivA_pvxHzGK1A0sYWLOWgn7aKLlsn5PGJC7o सदिश गुणनफल का परिचय (Cross product Introduction) सदिश गुणनफल का परिचय https://cdn.kastatic.org/ka-youtube-converted/qr94cdH8qhw.mp4/qr94cdH8qhw.mp4 947 सदिशों का सदिश गुणन (Cross product) https://hi.khanacademy.org/science/up-class-11-physics/x3a9a44f124d01cf7:system-of-particles-and-rotational-motion/x3a9a44f124d01cf7:cross-product-and-torque/v/cross-product-1 2023-05-19T06:09:43.239632101Z सदिश गुणनफल 1 (Cross Product 1) सदिश गुणनफल का परिचय Sal Khan video https://cdn.kastatic.org/googleusercontent/1dyRhyEsJB4tyLdePnXPP6yCsoQ3qzcPxXrkoZp2Tn2x3S65U3REboU7jPUy2QULW-0gMk4ods7hGKkSORtAA_7v0A सदिश गुणनफल 1 (Cross Product 1) सदिश गुणनफल का परिचय https://cdn.kastatic.org/ka-youtube-converted/cC_S8iHIfxQ.mp4/cC_S8iHIfxQ.mp4 602 सदिशों का सदिश गुणन (Cross product) https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:vector-algebra-ncert-new/x7ce8ca9c5869750b:cross-product-of-vectors-1/v/cross-product-2 2023-05-19T06:09:43.239632101Z सदिश गुणनफल 2 (Cross Product 2) A little more intuition on the cross product. Sal Khan video https://cdn.kastatic.org/googleusercontent/hterZg1rl5CpYA0mA-xkMGL9ie1tu0KODpCFM5Zw-ZsANODpxE9cDY_SmfqKLd87aMoUQPyZwt8OsSOkyJHyKShx सदिश गुणनफल 2 (Cross Product 2) A little more intuition on the cross product. https://cdn.kastatic.org/ka-youtube-converted/UYftfaCU1uY.mp4/UYftfaCU1uY.mp4 653 सदिशों का सदिश गुणन (Cross product) https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:vector-algebra-ncert-new/x7ce8ca9c5869750b:cross-product-of-vectors-1/e/cross-product-of-two-vectors 2026-04-08T08:46:38.570038857Z दो सदिशों का सदिश गुणनफल (Cross product) सदिश गुणनफल (Cross product) exercise https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:vector-algebra-ncert-new/x7ce8ca9c5869750b:cross-product-of-vectors-1/e/cross-product-of-two-vectors-advanced 2026-04-08T08:46:38.570038857Z दो सदिशों का सदिश गुणनफल (cross product) (एडवांस्ड) सदिश गुणनफल - लंबवत सदिश, सदिश गुणनफल के गुणधर्म और समांतर चतुर्भुज का क्षेत्रफल ज्ञात करें। exercise