Parallel to the z-axis refers to lines or planes that have the same direction as the z-axis in a three-dimensional coordinate system. These objects do not intersect the z-axis and their position is constant along the x and y coordinates. Examples include vertical lines or planes extending up and down.
Class 12 Maths Chapter 11 Three Dimensional Geometry is important for CBSE Exam 2024-25. It covers topics like direction cosines and direction ratios of a line equations of a line in different forms shortest distance between two lines equations of a plane angles between planes and distance of a point from a plane.
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A line parallel to the z-axis has constant x and y coordinates, while the z-coordinate changes. For a line passing through the point (1, 1, 1) and parallel to the z-axis, the x and y coordinates remain constant at 1, while the z-coordinate changes.
The parametric equation of the line is:
(x – 1)/0 = (y – 1)/0 = (z – 1)/1
Thus, the correct answer is:
(x – 1)/0 = (y – 1)/0 = (z – 1)/1
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