Calculating the Magnitude of a vector:
where:
v = vector
n = distance
Vector multiplication by scalar
Normalized Vectors
Vector Adding and Subtracting
Distance from one vector to another
Vector Dot Product
The dot product of two vectors is the sum of the products of corresponding components. This
results in a scalar:
Generally speaking, the dot product in any dimension tells how “similar” two vectors are; the
larger the dot product, the more similar the two vectors. Geometrically, we can be more precise
Projecting one vector onto another
Vector Cross Product
The other vector product, known as the cross product or outer product, applies to 3D vectors only.
Unlike the dot product, which yields a scalar and is commutative, the vector cross product yields a
3D vector and is not commutative.
Like the dot product, the term “cross product” comes from the symbol used in the notation: a×b.
We always write the cross symbol, rather than omitting it like we do with scalar multiplication.
The equation for the cross product is given by:
Complete list of linear algebra identities
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