Line segment {vector, mathematics} can have magnitude and direction.
length
Vectors have length {modulus, vector} {absolute value, vector}. Vectors {unit vector} can have length equal to one unit.
direction
Vectors have angle to x-axis {amplitude, vector}.
equality
Equal vectors have same sense, direction, and length but do not have to have same space position.
addition
To add two vectors, move vector {component} so initial end coincides with other-vector terminal end. Keep component vector parallel to original direction. Sum is vector resultant from first-vector initial end to component-vector terminal end.
To add two vectors, add corresponding coordinates to get resultant-vector coordinates: (1,2) + (3,4) = (4,6).
Vector addition is commutative and associative.
subtraction
To subtract vectors, first reverse direction of vector to subtract. Then add the vectors.
To subtract vectors, subtract corresponding coordinates: (1,2) - (3,4) = (-2,-2).
vector function
Ordered pairs can have real numbers as domain and vectors as range.
bundle
Vectors can have initial ends at same point {bound vectors} {bundle, vector} {vector, bundle}.
triangle of vectors
Two component vectors and their resultant make triangle {triangle of vectors}.
tensor
Vectors are rank-1 covariant tensors.
vector types
Vectors can have structures at termini. Structure can be another vector, such as a rotating vector. Structure can be a differential length, area, or volume.
Mathematical Sciences>Calculus>Vector
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Date Modified: 2022.0224