If two points are located on the same side of the coordinate axis, first find a symmetrical point, and the intersection of the straight line of the connection point and the symmetrical point and the coordinate axis is the solution. See the figure below:
A spatial coordinate system consisting of three-dimensional orthogonal spatial coordinate axes X, Y and Z can be established in the reference system.
The change of the spatial position of the material system relative to the spatial coordinate system in the acceleration field can be called displacement. The displacement is a vector, and the component of the displacement K from the origin O on the orthogonal coordinate axes X, Y and Z is k? , Ky, Kz, which means:
k？ =Kcosα
Ky= Kcosβ
Kz=Kcosγ
Where α, β and γ are the spatial azimuth angles formed by the displacement k and the positive directions of the spatial axes X, Y and Z, respectively.
Let I, J and K be unit vectors along the positive directions of the X, Y and Z axes, respectively, then the displacement k can be expressed as:
K = Kxi？ + Ky？ j？ + Kz？ k
The magnitude of the displacement k can be expressed as:
K = |K|
The cosine values of the included angles α, β and γ between the displacement k and the X, Y and Z axes can be expressed as:
cosα=cos∠KOAcos∠AOX= Kx/K
cosβ=cos∠KOAcos∠AOY=Ky/K
cosγ=cos∠KOCcos∠COZ=Kz/K
Extended data:
Analytic method can prove that the intersection of the midpoint line of two points on a straight line and the circle is the sum of the shortest distances.
Spatio-temporal displacement S can be decomposed into time component St and space component Sk in a two-dimensional spatio-temporal coordinate system composed of time coordinate axis T and displacement direction K in the spatial coordinate system.
Here, the temporal component St and the spatial component Sk are:
St=t=Scosθ
Sk=k=Scosφ, where θ and φ are the space-time angles formed by space-time displacement s, time axis t and space coordinate axis k, respectively.
Spatio-temporal displacement S can be decomposed into spatial component Sk in spatial coordinate system, which is a spatial vector, namely displacement vector K. Displacement K can be decomposed into spatial coordinate components Kx, Ky, Kz x, Y, Z,
Space-time displacement S can be decomposed into time component S t on the time coordinate axis, which has the same space-time direction as time unit vector H in the space-time coordinate system, so it can be called time vector. However, when describing the spatial motion of a material system, the spatial direction cannot be reflected as the coordinate time t, so the time component t is usually called a scalar in the spatial motion.
Space-time offset s can be expressed as:
S = St + Sk
S = St？ h？ + Kx？ Me? + Ky？ j？ + Kz？ k
The cosine of the angle between the space-time displacement s and the t, x, y and z axes can be expressed as:
cosθ= St / S
cos φx = Kx / S
cos φy = Ky / S
cos φz = Kz / S
Where: S = absolute value of space-time displacement.