Find the equation of lines passing through a point(2,1,3) and parallel to i)x-axis ii)y- axis?

Question

Answer

Equation of line=a(x-2)+b(y-1)+c(z-3) =0
line is parellel to X and y axis
then a=b=0
line=c(z-3)=0
z-3=0.

Answer

Equation of Lines Passing Through a Point and Parallel to Axes

Lines Parallel to x-axis:
- The equation of a line passing through the point (2,1,3) and parallel to the x-axis will have a constant x-coordinate, i.e., x = 2.
- Therefore, the equation of the line will be x = 2.

Lines Parallel to y-axis:
- The equation of a line passing through the point (2,1,3) and parallel to the y-axis will have a constant y-coordinate, i.e., y = 1.
- Therefore, the equation of the line will be y = 1.

Explanation:
- When a line is parallel to the x-axis, its slope is zero because it moves only along the x-axis.
- When a line is parallel to the y-axis, its slope is undefined because it moves only along the y-axis.
- In the given case, the lines passing through the point (2,1,3) and parallel to the x-axis or y-axis have a fixed value for one of the coordinates and can vary in the other coordinates.
- By understanding the nature of lines parallel to the axes, we can easily determine their equations passing through a given point.

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