Math Problem Statement
Solution
The image you've uploaded contains a question in Vietnamese about geometry in a three-dimensional space. Here's a translation of the problem:
Question 1:
In the space , given the line defined by the system:
and the plane defined by the equation:
Find the coordinates of the point such that the point lies on the line and the distance from to the plane is 3. Calculate .
Approach:
-
Parameterize the Line :
The equation for the line can be written as: where is the parameter. -
Substitute Coordinates of into the Plane Equation:
The point lies on the line, so substitute the parameterized coordinates into the plane equation: -
Find the Distance from Point to Plane :
The distance from a point to the plane is given by the formula: For this problem, we set and solve for the coordinates . -
Solve for :
Once the values for , , and are found, compute .
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Math Problem Analysis
Mathematical Concepts
Analytical Geometry
Distance from Point to Plane
Parameterization of a Line
Formulas
Distance from point to plane: d = |Ax1 + By1 + Cz1 + D| / sqrt(A^2 + B^2 + C^2)
Parameterization of a line
Theorems
Distance from a point to a plane formula
Suitable Grade Level
Grades 10-12
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