A projection in mathematics is a mathematical operation that maps a point or set of points onto a lower dimensional space. This is often done in order to simplify a problem or to visualize data in a more easily interpretable way.
An orthogonal projection is a type of projection where the projected vector is perpendicular to the projection plane. This means that the projected vector forms a right angle with the projection plane, resulting in a 2-dimensional image that is as close to the original 3-dimensional object as possible.
Orthogonal projection is different from other types of projections in that it preserves the distances between points in the original object, whereas other types of projections may distort the distances. It is also unique in that the projected vector is perpendicular to the projection plane.
Understanding projection in mathematics is important because it allows for the simplification of complex problems and the visualization of data in a more meaningful way. It is also a fundamental concept in geometry and can be applied in various fields such as physics, engineering, and computer graphics.
To improve your understanding of projection, it is important to first have a strong understanding of basic mathematics concepts such as vectors and matrices. You can also practice with different types of projections, visualize them, and apply them to real-life problems. Additionally, seeking guidance from a teacher or working through practice problems can also help improve your understanding.