 # Vector projection using Python

Vector — it is a geometric object that has both magnitude (that is, length) and direction. The vector is usually represented by a line segment with a specific direction connecting the start point A and the end point B, as shown in the figure below, and is denoted as  ## Projection of a vector onto another vector

Projection of a vector to another vector given as Calculate vector projection onto another vector in Python:

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``` # import numpy to perform vector operations import numpy as np   u = np.array ([ 1 , 2 , 3 ])  # vector you v = np .array ([ 5 , 6 , 2 ])  # vector v:   # Problem: Project vector u on vector v   # find the norm of the vector v v_norm = np. sqrt ( sum (v * * 2 ))    # Apply the formula as above # to project the vector onto another vector # find point product using np.dot () proj_of_u_on_v = (np.dot (u, v) / v_norm * * 2 ) * v   print ( " Projection of Vector u on Ve ctor v is: " , proj_of_u_on_v) Exit: Projection of Vector u on Vector v is: [1.76923077 2.12307692 0.70769231] One line code to project a vector onto another vector: (np.dot (u, v) / np.dot (v, v)) * v ```

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## Vector projection onto plane

Vector projection the plane is calculated by subtracting the component which is orthogonal plane from ,

where, is a flat normal vector .

Calculate vector projection on a plane in Python:

 ` # import numpy to perform vector operations ` ` import ` ` numpy as np ` ` `  ` # vector you ` ` u ` ` = ` ` np.array ([` ` 2 ` `, ` ` 5 ` `, ` ` 8 ` ` ]) `   ` # vector n: n - ortho gonal vector to plane P ` ` n ` ` = ` ` np.array ([` ` 1 ` `, ` ` 1 ` `, ` ` 7 ` `]) ` ` `  ` # Problem: Project vector u on the P plane ` ` `  ` # find the norm of the vector n ` ` n_norm ` ` = ` ` np.sqrt (` ` sum ` ` (n ` ` * ` ` * ` ` 2 ` `)) `   ` # Apply the formula as above ` ` # for project vector to orthogonal vector n ` ` # find point product using np.dot () ` ` proj_of_u_on_n ` ` = ` ` (np.dot (u, n) ` ` / ` ` n_norm ` ` * ` ` * ` ` 2 ` `) ` ` * ` ` n `   ` # subtract from you proj_of_u_on_n: ` ` # this is your projection onto the P plane ` ` print ` ` (` ` "Projection of Vector u on Plane P is:" ` `, u ` ` - ` ` proj_of_u_on_n) `

Output:

` Projecti on of Vector u on Plane P is: [0.76470588 3.76470588 -0.64705882] `