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A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "carrier". [4] It was first used by 18th century astronomers investigating planetary revolution around the Sun. [5] The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from A to B.
In an axiomatic formulation of Euclidean geometry, such as that of Hilbert (modern mathematicians added to Euclid's original axioms to fill perceived logical gaps), [1]: 108 a line is stated to have certain properties that relate it to other lines and points. For example, for any two distinct points, there is a unique line containing them, and ...
A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "carrier". [4] It was first used by 18th century astronomers investigating planetary revolution around the Sun. [5] The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from A to B.
Relative velocities between two particles in classical mechanics. The figure shows two objects A and B moving at constant velocity. The equations of motion are: = +, = +, where the subscript i refers to the initial displacement (at time t equal to zero).
In P 2, the line between the points x 1 and x 2 may be represented as a column vector ℓ that satisfies the equations x 1 T ℓ = 0 and x 2 T ℓ = 0, or in other words a column vector ℓ that is orthogonal to x 1 and x 2. The cross product will find such a vector: the line joining two points has homogeneous coordinates given by the equation ...
In geometry, a normal is an object such as a line or vector that is perpendicular to a given object. For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.
Displacement is the shift in location when an object in motion changes from one position to another. [2] For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude is the average speed (a scalar quantity).
In a manner analogous to the way lines in a two-dimensional space are described using a point-slope form for their equations, planes in a three dimensional space have a natural description using a point in the plane and a vector orthogonal to it (the normal vector) to indicate its "inclination".