Orthogonal projection is a mathematical concept that involves projecting a vector or shape onto a plane or subspace in a way that preserves the right angles between the original vector and the projected vector.
A triangle V, v'_{1} is a triangle with three vertices, V, and a vector v'_{1} that is perpendicular to one of the sides of the triangle.
To prove orthogonal projection of a triangle V, v'_{1}, you can use the Pythagorean theorem and the dot product to show that the projected vector is perpendicular to the original vector and that the length of the projected vector is equal to the length of the original vector multiplied by the cosine of the angle between them.
Orthogonal projection has many applications in fields such as engineering, computer graphics, and physics. It is used to create 3D models, map objects onto surfaces, and calculate forces and velocities in mechanics.
Orthogonal projection is unique in that it preserves the angles between the original vector and the projected vector, whereas other types of projections may distort or change these angles. It is also a special case of a more general concept called vector projection.