 Vector Questions,
a selection of answers from the Dr. Math archives.
 What is a Vector?
 I am having trouble understanding exactly what a vector is and
cannot seem to find a simple, straightforward explanation.
 Definition of a Vector
 I would like a "proper" definition of a vector and how concepts of
"magnitude" and "direction" arise in the discussion of vectors.
 Sum of Two Vectors
 Why is the magnitude of the sum of two vectors less than or equal
to the sum of the magnitudes of each vector?
 Using Vectors in Geometry and
Physics
 How do you use vectors in problems about medians, areas, and
acceleration and velocity?
 Vector Algebra: Finding the
Intersection Point
 If I have two lines in three dimensions that I know intersect at some
point, how do I work out what that point is? Both lines are defined by
two points on each line.
 Unit Vectors
 Find the two unit vectors that are collinear with each of the
following vectors. (a) vector A = (3, 5). I don't understandis a unit
vector only ever equal to 1?
 Equation for Angle Formed by
Two Vectors
 Do I need to find the vector equation of OP and OQ, or of PO and OQ,
when finding the angle POQ using the formula cos(theta)=a.b/ab?
 Angle Between Vectors
 Given vectors A and B in a plane, and vector C normal to that plane,
compute the clockwise angle from vector A to vector B when viewed in
the direction of the normal vector C.
 Find the Velocity  a Vector
Problem
 A river flows westward at 8 m/s. A person wants to go directly across
the river so that the resultant velocity is 12 m/s northward. Find the
velocity of the motorboat that would be required to achieve this resultant
velocity.
 Vectors of Parallelograms and
Octagons
 ABCDEFGH is a regular octagon and AB = p and BC = q. Express AH in
terms of p and q...
 Vectors and Orientation
 I am trying to write a game involving spaceships, and I have been
having trouble finding relative positions.
 ThreeDimensional Vectors
 I am finding it very hard to understand and visualise the notion of
a vector in 3 dimensions.
 The Stationary Vector
 In Markov processes, what does a stationary vector tell you and
how do you find it?
 Rotación de Véctores
(3D Vector Rotation)
 Hay alguna fórmula para rotar véctores en el espacio
sobre los tres ejes de coordenadas?
 Intersecting Vectors and the
Dot Product
 Each of the following geometrical theorems can be proved with
vectors, using the dot product...
 Distance Between a Line and a
Point Using Vectors
 How do you use scalar vector projections to prove that the distance
between the line ax+by+c = 0 and point (x1,y1) is
ax1+by1+c/sqrt(a^2+b^2)?
 Distance Between 2 Lines: Vectors
 What is the shortest distance between 2 lines?
 Vector Proofs
 Vector Proof
 Prove that given P, Q, R, and S (any 4 noncollinear points), with
A and B the midpoints of PR and QS respectively, then PQ + RS = 2 AB...
 Vector Proof: Parallelogram
Diagonals
 Use vectors to prove that the diagonals of a parallelogram bisect
each other and the line joining the midpoints of two sides of a triangle...
 Vector Space
 Understanding Vector Spaces
 What does a vector space in R^n mean? How can I prove that a list of
numbers is a vector space?
 Vector Spaces
 How can I tell if V = {(x,y) in R^2  y = 3x+1} a vector space when
addition and scalar multiplication are defined by (x,y) + (x',y') =
(x+x',y+y'1) and k(x,y) = (kx,k(y1)+1)?
 Vector Space Dimensions
 Why does C^2 considered as a vector space over the complex numbers
have dimension 2, but as a vector space over the real numbers have
dimension 4?
 Basis for a Vector Space in R^3
 Are the following bases for R^3: {(2,3,1), (4,1,1), (0,7,1)} ... ?
