The formula for calculating the distance from point to plane is: d = lax0+by0+cz0 +d|/(a2+b2+c2). Where (x0y0, z0) is the coordinate of the point, and ax+by+cz+d=0 is the analytic formula of the plane.
This formula looks complicated, but it is actually just a simple vector operation. The distance from point P(x0y0z0) to plane Ax+By+Cz+D=0 can be transformed into vector form, that is, d = | (p-P0) n |/| n |. Where PO is any point on the plane, n=(ABC) is the normal vector of the plane, and P-PO is the difference of the vectors.
The principle of this formula is to convert the distance from point P to plane into the distance from point P to point PO on the plane, and then calculate the distance by using the inner product operation of vectors.
This formula is widely used in geometry, such as finding the distance from a point to a straight line, from a point to a plane, from a straight line to a plane and so on. In physics, the distance formula from point to surface also has important applications. For example, when calculating the propagation of light in different media, the distance formula from point to surface is needed.
The formula of distance from point to surface is an important knowledge point in high school mathematics. Mastering this formula can help us better understand various problems in geometry and physics and provide convenience for our study and research.
Learning math well has many advantages.
1, improve logical thinking ability: Mathematics is a rigorous subject, and learning mathematics can exercise the logic and rigor of thinking and cultivate the ability to analyze and solve problems.
2. Enhance the ability of abstract thinking: Mathematics involves abstract concepts and symbols. Learning mathematics can train people's abstract thinking ability and improve their ability to understand and solve abstract problems.
3. Cultivate creativity: Mathematics is a creative subject. Learning mathematics can cultivate people's creative thinking and innovative ability, and encourage students to put forward new solutions and ideas.