Vectors - Math is Fun
网页Velocity, acceleration, force and many other things are vectors. Subtracting. We can also subtract one vector from another: first we reverse the direction of the vector we want to subtract, then add them as usual: a − b. Notation. A vector is often written in bold, like a or b.
Scalars and Vectors - Math is Fun
网页Scalars, Vectors and Matrices. And when we include matrices we get this interesting pattern: A scalar is a number, like 3, -5, 0.368, etc, A vector is a list of numbers (can be in a row or column), A matrix is an array of numbers (one or more rows, one or more columns). In fact a vector is also a matrix!
Dot Product - Math is Fun
网页The dot product of two vectors that point in the same direction is the simple product of their lengths, because the angle is 0 degrees which has a cosine of 1. a · b = | a | × | b | × cos (0°) a · b = a × b × 1. a · b = ab.
Cross Product - Math is Fun
网页The Cross Product gives a vector answer, and is sometimes called the vector product. But there is also the Dot Product which gives a scalar (ordinary number) answer, and is sometimes called the scalar product.
Vector Calculator - Math is Fun
网页Enter values into Magnitude and Angle ... or X and Y. It will do conversions and sum up the vectors. Learn about Vectors and Dot Products.
Unit Vector - Math is Fun
网页Unit vectors can be used in 2 dimensions: Here we show that the vector a is made up of 2 "x" unit vectors and 1.3 "y" unit vectors.
Eigenvector and Eigenvalue - Math is Fun
网页Notice how we multiply a matrix by a vector and get the same result as when we multiply a scalar (just a number) by that vector.
Vector Definition (Illustrated Mathematics Dictionary) - Math is Fun
网页Illustrated definition of Vector: A vector has magnitude (how long it is) and direction. Play with one below:
Component (vector) Definition (Illustrated Mathematics Dictionary)
网页When we break a vector into two or more parts, each of those new vectors is a component of the original vector. See how a vector can be broken into x and y components here:
Commutative, Associative and Distributive Laws - Math is Fun
网页The "Distributive Law" is the BEST one of all, but needs careful attention. This is what it lets us do: 3 lots of (2+4) is the same as 3 lots of 2 plus 3 lots of 4. So, the 3× can be "distributed" across the 2+4, into 3×2 and 3×4. And we write it like this: a × (b + c) = a × b + a × c. Try the calculations yourself: