By Kardi Teknomo, PhD .
LinearAlgebra

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Suppose we have a vector Vector Projection in 2-dimensional space, and we would like to find the component of vector Vector Projection in the direction of horizontal and vertical axis. Using trigonometry we can find the magnitude of vector component to be Vector Projection and Vector Projection . The direction of these vector components are the standard unit vector of horizontal and vertical axes Vector Projection and Vector Projection .
Vector Projection

We can find vector projection of a vector Vector Projection onto other vector Vector Projection based on the inner product of the two vectors. Scalar projection of vector Vector Projection onto vector Vector Projection is the magnitude of projection given as Vector Projection . Vector projection of vector Vector Projection onto vector Vector Projection is the magnitude of projection times the unit vector of Vector Projection becomes Vector Projection . Geometrically, vector projection is shown in the figure below.
Vector Projection

Example
Projection of vector Vector Projection onto horizontal axis is equivalent to projection of vector Vector Projection onto unit standard vector Vector Projection . The scalar projection is Vector Projection . The projection vector becomes Vector Projection . Cosine angle between two vectors is Vector Projection . Thus, Vector Projection .

The interactive program below will give you the projection vectors and the scalar projection. You need to provide 2 vectors as the input. Random Example button will generate random input vectors.

vector x vector y

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