Search results
Results from the WOW.Com Content Network
Illustration of the vector formulation. The equation of a line can be given in vector form: = + Here a is the position of a point on the line, and n is a unit vector in the direction of the line. Then as scalar t varies, x gives the locus of the line.
The normal form of the equation of a straight line on the plane is given by: + =, where is the angle of inclination of the normal segment (the oriented angle from the unit vector of the x-axis to this segment), and p is the (positive) length of the normal segment.
If V is a topological vector space, then a closed line segment is a closed set in V. However, an open line segment is an open set in V if and only if V is one-dimensional. More generally than above, the concept of a line segment can be defined in an ordered geometry.
[9] [12] Bound vector quantities are formulated as a directed line segment, with a definite initial point besides the magnitude and direction of the main vector. [ 9 ] [ 11 ] For example, a force on the Euclidean plane has two Cartesian components in SI unit of newtons and an accompanying two-dimensional position vector in meters, for a total ...
A Euclidean vector is thus an equivalence class of directed segments with the same magnitude (e.g., the length of the line segment (A, B)) and same direction (e.g., the direction from A to B). [14] In physics, Euclidean vectors are used to represent physical quantities that have both magnitude and direction, but are not located at a specific ...
The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as proj b a {\displaystyle \operatorname {proj} _{\mathbf {b} }\mathbf {a} } or a ∥ b .
The vector equation for a line is = + where is a unit vector in the direction of the line, is a point on the line, and is a scalar in the real number domain. Substituting the equation for the line into the equation for the plane gives
Three line segments with the same direction. In geometry, direction, also known as spatial direction or vector direction, is the common characteristic of all rays which coincide when translated to share a common endpoint; equivalently, it is the common characteristic of vectors (such as the relative position between a pair of points) which can be made equal by scaling (by some positive scalar ...