Class 12 Basic Mathematics Co-ordinate in Space Solution and Guide

The study of coordinates in space introduces students to the three-dimensional (3D) coordinate system, which is a significant topic in Class 12 Basic Mathematics. This concept forms the foundation for advanced studies in geometry, physics, and engineering, providing tools to analyze objects and movements in three dimensions. To help students excel in this subject, we present the Class 12 Basic Mathematics Co-ordinate in Space Solution and Guide.

This guide aligns with the Class 12 Basic Mathematics textbook approved by the Curriculum Development Center of Nepal. It offers detailed explanations, practical problem-solving strategies, and a thorough exploration of the topic to prepare students for NEB examinations and assignments.

Understanding Coordinates in Space

Coordinates in space use the three-dimensional Cartesian coordinate system, represented by three axes: $x$-axis, $y$-axis, and $z$-axis. Any point in space can be defined using an ordered triplet $(x,y,z)$, which specifies its location relative to these axes.

Key concepts covered in this guide include:

1. Distance Formula: Calculating the distance between two points in 3D space using:$$d=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2+(z_2-z_1{)}^2}$$
   
2. Midpoint Formula: Finding the midpoint between two points in space:$$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2})$$
   
3. Equation of a Line in Space:
   • Symmetric form.
   • Parametric form.
4. Equation of a Plane: Understanding the general form $ax+by+cz+d=0$ and how to derive it given specific conditions.

Key Features of the Guide

Comprehensive Explanations:
Detailed derivations and theoretical explanations help students understand the principles of 3D geometry and their applications.

Visual Representations:
Graphical illustrations clarify the spatial relationships between points, lines, and planes.

Step-by-Step Solutions:
Worked-out examples demonstrate how to solve typical problems, such as finding distances, midpoints, angles between planes, and intersections of lines and planes.

Applications:
Real-life examples show how 3D geometry is used in navigation, architecture, and engineering design.

Practice Problems:
Additional exercises with solutions are provided to enhance students' problem-solving skills and build confidence.

Download and Share

This article includes a downloadable PDF of the guide, making it convenient for students to access and study anytime. The guide is designed for assignments, exam preparation, and improving conceptual understanding. Sharing the guide with friends can promote collaborative learning and ensure comprehensive preparation for the NEB examinations.

The Class 12 Basic Mathematics Co-ordinate in Space Solution and Guide simplifies complex concepts, provides practical strategies, and ensures students are well-equipped for academic success. Download the guide today, share it with your peers, and confidently master 3D geometry for your examinations and beyond!

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