NCERT solution Class 11 introduction to three dimensional geometry

NCERT Solutions

Class 11 Maths

Introduction to Three Dimensional Geometry

NCERT Questions

Ex.12.1 Q.1
Ex.12.1 Q.2
Ex.12.1 Q.3
Ex.12.1 Q.4
Ex.12.2 Q.1
Ex.12.2 Q.2
Ex.12.2 Q.3
Ex.12.2 Q.4
Ex.12.2 Q.5
Ex.12.3 Q.1
Ex.12.3 Q.2
Ex.12.3 Q.3
Ex.12.3 Q.4
Ex.12.3 Q.5
Misc. Q.1
Ex.Misc. Q.2
Ex.Misc. Q.3
Ex.Misc. Q.4
Ex.Misc. Q.5
Ex.Misc. Q.6

Ex.12.3 Q.5

Find the coordinates of the points which trisect the line segment joining the points P (4, 2, –6) and Q (10, –16, 6).

Let A and B be the points that trisect the line segment joining points P (4, 2, –6) and Q (10, –16, 6).

Point A divides PQ in the ratio 1: 2. Therefore, by section formula, the coordinates of point A are given by

{(1 × 10 + 2 × 4) ÷ (1 + 2), (-16 × 1 + 2 × 2) ÷ (1 + 2), (1 × 6 + 2 × (-6)) ÷ (1 + 2)} = (6, -4, -2)

Point B divides PQ in the ratio 2: 1. Therefore, by section formula, the coordinates of point B are given by

{(2 × 10 + 1 × 4) ÷ (2 + 1), (-16 × 1 + 2 × 1) ÷ (2 + 1), (2 × 6 + 1 × (-6)) ÷ (2 + 1)} = (8, -10, 2) Thus, (6, –4, –2) and (8, –10, 2)

are the points that trisect the line segment joining points P (4, 2, –6) and Q (10, –16, 6).

Introduction to Three Dimensional Geometry Class 11 Maths NCERT Chapter 11 NCERT Solutions

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Attempt to Solve Yourself: Before looking at the solution, try to solve or answer the question independently. This practice will help you test your knowledge and problem-solving skills.
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Refer to Solution Video (if needed): If you encounter difficulty or are unable to solve a question, you can refer to the NCERT solution video on Introduction to Three Dimensional Geometry Class 11 Maths NCERT Chapter 11 to get a step-by-step explanation of the correct approach. Pay attention to the reasoning and methodology used in the video.
Solve Again Yourself: Once you've understood the solution, attempt to solve the question again by yourself. Repetition and practice solidify your understanding of the concepts and improve retention.
Avoid Memorization: Focus on understanding the underlying principles and concepts behind each solution. Avoid simply memorizing the solutions, as this may hinder your ability to apply the knowledge in different contexts.
Attempt All Questions: Make an effort to attempt all the questions provided in the NCERT textbook. This comprehensive practice will help you cover the entire syllabus and reinforce your understanding across various topics. You may refer Class 11 Maths Introduction to Three Dimensional Geometry Online Test on LearnoHub.com.
Review and Revise: Regularly review the concepts and solutions you've learned. Revise your notes and practice regularly to retain the knowledge effectively. You may refer Introduction to Three Dimensional Geometry Class 11 Maths Notes.
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NCERT solutions of Introduction to Three Dimensional Geometry Class 11 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 11 Maths Introduction to Three Dimensional Geometry NCERT solutions.