The angle between the lines whose direction ratios are proportional to a², b², c² and b² – c², c² – a², a² – b² is
Proportional refers to a relationship between two quantities where a change in one quantity results in a corresponding change in the other. If two quantities are proportional they increase or decrease at the same rate. The concept is often used in mathematics physics and economics to express ratios and relationships.
Class 12 Maths Chapter 11 Three Dimensional Geometry is essential for CBSE Exam 2024-25. It covers topics like direction cosines and direction ratios of a line equations of a line in various forms shortest distance between two lines equations of a plane angles between planes and distance of a point from a plane.
Share
The direction ratios of the two lines are given as:
Line 1: a², b², c²
Line 2: b² – c², c² – a², a² – b²
The angle θ between two lines is given by the formula:
cos θ = (l₁l₂ + m₁m₂ + n₁n₂) / √(l₁² + m₁² + n₁²) * √(l₂² + m₂² + n₂²)
Substituting the direction ratios into the formula:
cos θ = [(a²)(b² – c²) + (b²)(c² – a²) + (c²)(a² – b²)] / √[(a²)² + (b²)² + (c²)²] * √[(b² – c²)² + (c² – a²)² + (a² – b²)²]
After simplifying the expression, we get cos θ = 0, which means θ = π/2.
Thus, the correct answer is: π/2
Click here for more:
https://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-11