Geometry is a branch of mathematics that deals with shapes sizes and the properties of space. It studies points lines angles surfaces and solids. Geometry is divided into plane geometry involving flat shapes like circles and triangles and solid geometry dealing with three-dimensional objects like spheres and cubes.
Class 12 Maths Chapter 11 Three Dimensional Geometry is crucial for CBSE Exam 2024-25. It covers 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.
Share
The given equations of the lines can be written in parametric form:
For the first line:
2x = 3y = -z, let the parameter be t.
x = t/2, y = t/3, z = -t.
For the second line:
6x = -y = -4z, let the parameter be s.
x = s/6, y = -s, z = -s/4.
The direction ratios of the first line are (1/2, 1/3, -1) and the direction ratios of the second line are (1/6, -1, -1/4).
The angle θ between two lines is given by the formula:
cos θ = (l₁l₂ + m₁m₂ + n₁n₂) / √(l₁² + m₁² + n₁²) * √(l₂² + m₂² + n₂²)
Substitute the values:
cos θ = [(1/2)(1/6) + (1/3)(-1) + (-1)(-1/4)] / √[(1/2)² + (1/3)² + (-1)²] * √[(1/6)² + (-1)² + (-1/4)²]
Simplifying this expression results in cos θ = 0, so the angle θ = 90°.
Thus, the correct answer is: 90°
Click here for more:
https://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-11