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Math Vectors Video

Vectors - GCSE Maths

Math Vectors - something

This is a basic, though hopefully fairly comprehensive, introduction to working with vectors. Vectors manifest in a wide variety of ways from displacement, velocity, and acceleration to forces and fields. This article is devoted to the mathematics of vectors; their application in specific situations will be addressed elsewhere. A vector quantity , or vector , provides information about not just the magnitude but also the direction of the quantity. When giving directions to a house, it isn't enough to say that it's 10 miles away, but the direction of those 10 miles must also be provided for the information to be useful. Variables that are vectors will be indicated with a boldface variable, although it is common to see vectors denoted with small arrows above the variable. Just as we don't say the other house is miles away, the magnitude of a vector is always a positive number, or rather the absolute value of the "length" of the vector although the quantity may not be a length, it may be a velocity, acceleration, force, etc. A negative in front a vector doesn't indicate a change in the magnitude, but rather in the direction of the vector. Math Vectors

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for Mwth, skills, Math Vectors videos. Math Linear algebra Vectors and spaces Vector dot and cross products.

Vector dot and cross products

Vector dot product and vector length. Proving vector dot product properties. Proof of the Cauchy-Schwarz inequality. Vector triangle inequality. Defining the angle between vectors.

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Defining a plane in R3 with a point and normal vector. Cross product introduction. Proof: Relationship between https://amazonia.fiocruz.br/scdp/blog/woman-in-black-character-quotes/melting-pot-theory.php product and sin of angle. Vector triple product expansion very optional. Normal vector from plane equation. Point distance to plane. Vecrors between planes. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript We've already made a few definitions of Math Vectors that we can do with vectors. We've defined addition in the context of Math Vectors and you've seen that. If you just have two vectors, say a1, a2, all the way down to a n.

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We defined the addition of this vector and let's say some other vector, b1, b2, all the way down to bn as a third Vectlrs. If you add these two, we defined the addition operation to be a third-- you will result in a third vector where each of its components are just the sum of the Math Vectors components of the two vectors you're adding. So it's going to be a1 plus b1, a2 plus b2, all the way down to a n plus bn. We knew this and we've done Vecgors videos where we use this definition of vector addition. We also know about scalar multiplication. Maybe we should just call it scaling multiplication. And that's the case of look, if I have some real number c and I multiply it times some vector, a1, a2, all the way down to a n, we defined scalar multiplication of a vector to be-- some scalar times its vector will result in essentially, Math Vectors vector Math Vectors each of its components are multiplied by the scalar.

And so after seeing these two operations, you might be tempted to say, gee, wouldn't it be nice if there was some way to multiply two vectors. This is just a scalar Vrctors a vector, just scaling it up. And that's actually the actual effect of what it's doing if you visualize it in three dimensions Math Vectors less. It's actually scaling the size of the vector. And we haven't defined size, very precisely just Math Vectors.

But you understand at least this operation. For multiplying vectors or taking the product, there's actually two ways.

And I'm going to define one of them in this video. And that's the dot product. And you signify the dot product by saying a dot b.]