Question

Дан куб авсда1в1с1д1 Р принадлежит вв1 ВР=В1Р. как построить точку пересечения плоскости авс с прямой Д1Р

Answer 1

Строим прямую ДВ и пересекаем ее с прямой Д1Р, это и есть точка

Answer 2

Finding the Intersection Point of Plane AVS and Line D1R

To find the intersection point of the plane AVS and the line D1R, we can use the equations of the plane and the line to solve for the coordinates of the intersection point.

Equation of the Plane AVS: The equation of a plane in 3D space can be represented in the form Ax + By + Cz = D, where (A, B, C) is the normal vector to the plane, and (x, y, z) are the coordinates of a point on the plane.

Equation of the Line D1R: The equation of a line in 3D space can be represented in parametric form as x = x1 + at, y = y1 + bt, z = z1 + ct, where (x1, y1, z1) are the coordinates of a point on the line, and (a, b, c) are the direction ratios of the line.

Steps to Find the Intersection Point:

1. Write the Equations: Write down the equation of the plane AVS and the equation of the line D1R in the standard form.

2. Substitute the Line Equation into the Plane Equation: Substitute the parametric equations of the line into the equation of the plane to find the value of the parameter (t) at the intersection point.

3. Find the Coordinates: Once you have the value of the parameter (t), substitute it back into the parametric equations of the line to find the coordinates of the intersection point.

Example Calculation:

For example, if the equation of the plane AVS is 2x + 3y - z = 6 and the equation of the line D1R is x = 1 + 2t, y = 3 - t, z = 4t, we can follow these steps to find the intersection point.

1. Substitute the line equations into the plane equation: 2(1 + 2t) + 3(3 - t) - (4t) = 6

2. Solve for the parameter (t): After solving the equation, we get the value of t.

3. Find the coordinates of the intersection point: Substitute the value of t back into the parametric equations of the line to find the coordinates of the intersection point.

By following these steps, you can find the exact coordinates of the intersection point between the plane AVS and the line D1R.