3D Geometry
Three Dimensional Geometry
star_batch_jee_advanced_2025
Grade None
Question:
If $l, m, n$ represent direction cosines (if we can call it) of a vector $\overrightarrow{OP}$, then which of the following relations holds?
l^2 + m^2 + n^2 = 1
l + m + n = 1
|l + m + n| = 1
|l| + |m| + |n| = 1
Step-by-Step Solution
Key Concept: Distance in this definition is the ratio of one coordinate's absolute value to the sum of all three absolute values.
The new definition of distance is $l = \frac{|x|}{|x|+|y|+|z|}$, which normalizes distance by the sum of absolute coordinates. This differs from Euclidean distance by using taxicab-like normalization instead of squared terms.
Correct Answer: 1