Zaymiey

📐 Mathematics  ·  Introduction to Three Dimensional Geometry  ·  JEE

Why can the 2D test for collinearity using slopes not be carried over directly to three dimensions?

Answer: A line in space has no single slope, since it makes three separate angles with the axes.

  • A A line in space has no single slope, since it makes three separate angles with the axes
  • B Slopes only exist for lines passing through the origin in any dimension
  • C Three points in space can never be collinear in the majority of documented cases
  • D Slope is undefined whenever any coordinate is negative under usual circumstances

Correct answer: A. A line in space has no single slope, since it makes three separate angles with the axes

Explanation: In 2D a line has one slope; in space its direction needs three numbers (direction ratios), so collinearity is tested with distances or proportional direction ratios instead.

zxyOP(x, y, z)first octant:x>0, y>0, z>0

Concept context

Coordinate axes and planes in space, octants, distance between two points, and the section formula

Read the full Introduction to Three Dimensional Geometry notes →