Vector dot product and vector length | Vectors and spaces | Linear Algebra | Khan Academy
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Definitions of the vector dot product and vector length Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/proving-vector-dot-product-properties?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra Missed the previous lesson? https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/subspace_basis/v/linear-algebra-basis-of-a-subspace?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
Comments
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সালাম বস !!!
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I was initially confused because I was watching this video to help write a custom function to find the dot product but Unity defines the dot product as "the magnitudes of the two vectors multiplied together and then multiplied by the cosine of the angle between them." I learned that there are two methods to find a dot product, although this video only mentions one of them, while Unity uses the other. Both methods yield the same result.
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"Hopefully you are taking this BEFORE college..." looks around so is it bad that I'm gonna graduate next semester and I'm just now taking this class? :O
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You really didn't think it would be useful to explain what a dot product actually represents and why you might use it?!
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Thanks!
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You don't seem to annotate your videos with links but ~7:38 would be an excellent place to link to a video on metrics if you have made one (I haven't checked, but I bet it's there)
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Did u represent the vector as column vector in matrix form? Im confused how u took product (dot) of 2x1 by 2x1 matrix, as no. of columns of 1st matrix is not equal to number of rows in second?
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can anyone answer this? htt p :// i.imgur. com/fiCGDtz. jpg
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A.B = AB cos (angle) means that the net force is a combination of 1] Force of A 2] Force of B 3] Angle at which A and B are clashing into each other. Cos is a measure of how parallel two forces are, hence cos(0) = maximum =1. And Cos comes in mathematics wherever two objects produce maximum impact when they are parallel to each other. There is a video on this on my channel. Hope this helps. BINNOY Visualizing Maths(moving beyond formulas) Available at Amazon and Kindle for 4$
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Vector dot, doctor vet
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Ya, I also realized that, 5 minutes later.
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Yes.
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Is it compulsory that the the multi-dimensions other than 3d space would be perpendicular to each other ?
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I'm interested in representing a known length and direction (in 3 dimensions) as a unique vector. I'll keep watching.
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nah
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Just MS paint I think lol
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@sahayester that's a program coming with an external hardware called drawing pad. So he draws it on the pad and pad sends drawings to pc instantly =)
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Thank you so much!! You are part of the reason I passed my first semester in year 10 :D
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can i marry your brain..
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What software is that
9m 10sLenght
311Rating