If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are
An angle is formed when two rays or lines originate from a common point called the vertex. Angles are measured in degrees or radians and classify into types such as acute, right, obtuse and reflex. Angles play a crucial role in geometry trigonometry and various mathematical applications.
Class 12 Maths Chapter 11 Three Dimensional Geometry is a key topic for CBSE Exam 2024-25. It includes concepts 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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The direction cosines of a line are the cosines of the angles it makes with the x, y, and z axes.
Given the angles:
– θ₁ = 90° with the x-axis, so cos(θ₁) = 0
– θ₂ = 135° with the y-axis, so cos(θ₂) = -1/√2
– θ₃ = 45° with the z-axis, so cos(θ₃) = 1/√2
Thus, the direction cosines are:
0, -1/√2, 1/√2
Therefore, the correct answer is:
0, -1/√2, 1/√2
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