IIT JEE Main Maths -Unit 11- Coordinates of a point in space- Study Notes-New Syllabus
IIT JEE Main Maths -Unit 11- Coordinates of a point in space – Study Notes – New syllabus
IIT JEE Main Maths -Unit 11- Coordinates of a point in space – Study Notes -IIT JEE Main Maths – per latest Syllabus.
Key Concepts:
- Three Dimensional Geometry: Coordinates of a Point in Space
Three Dimensional Geometry: Coordinates of a Point in Space
In three-dimensional geometry, every point in space is represented using three numbers called its coordinates. A point \( P \) is written as \( P(x, y, z) \), where:
- \( x \) → distance along the X-axis
- \( y \) → distance along the Y-axis
- \( z \) → distance along the Z-axis
The three axes \( X, Y, Z \) are mutually perpendicular and intersect at a common point called the origin \( O(0,0,0) \).
Coordinate Axes and Coordinate Planes
- X-axis: positive rightward, negative leftward
- Y-axis: positive forward, negative backward
- Z-axis: positive upward, negative downward
There are three coordinate planes:
- XY-plane : all points with \( z = 0 \)
- YZ-plane : all points with \( x = 0 \)
- Z X-plane : all points with \( y = 0 \)
Octants
The three coordinate planes divide space into 8 regions called octants.
- 1st octant : \( x > 0, y > 0, z > 0 \)
- Other octants follow by changing the signs of \( x, y, z \)
Distance of a Point From the Coordinate Planes
For a point \( P(x, y, z) \):
- Distance from XY-plane = \( |z| \)
- Distance from YZ-plane = \( |x| \)
- Distance from ZX-plane = \( |y| \)
Sign Convention (Very Important for JEE)
- If \( x > 0 \) → point is to the right of the YZ-plane
- If \( y > 0 \) → point is in front of the ZX-plane
- If \( z > 0 \) → point is above the XY-plane
Coordinates of Mid-Point in 3D
If \( A(x_1, y_1, z_1) \) and \( B(x_2, y_2, z_2) \), then midpoint \( M \) is:
\( M\left( \dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}, \dfrac{z_1 + z_2}{2} \right) \)
Coordinates of a Point Dividing a Line (Section Formula)
Point \( P \) dividing \( A(x_1, y_1, z_1) \) and \( B(x_2, y_2, z_2) \) in ratio \( m:n \) internally:
\( P\left( \dfrac{mx_2 + nx_1}{m+n}, \dfrac{my_2 + ny_1}{m+n}, \dfrac{mz_2 + nz_1}{m+n} \right) \)
Distance Between Two Points
If \( P_1(x_1, y_1, z_1) \) and \( P_2(x_2, y_2, z_2) \), then:
\( P_1P_2 = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2 + (z_2 – z_1)^2} \)
Example
Find the distance of the point \( P(3, -4, 5) \) from the XY-plane.
▶️ Answer / Explanation
Distance from XY-plane depends only on \( z \).
Given \( z = 5 \).
Distance = \( |5| = 5 \)
Example
Find midpoint of points \( A(2, 3, 5) \) and \( B(6, -1, 9) \).
▶️ Answer / Explanation
Midpoint = \( M\left( \dfrac{2+6}{2}, \dfrac{3 + (-1)}{2}, \dfrac{5+9}{2} \right) \)
= \( M(4, 1, 7) \)
Example
Find the distance between \( P(1,2,3) \) and \( Q(4,6,3) \).
▶️ Answer / Explanation
\( PQ = \sqrt{(4-1)^2 + (6-2)^2 + (3-3)^2} \)
= \( \sqrt{3^2 + 4^2 + 0^2} = \sqrt{25} = 5 \)
Notes and Study Materials
- Concepts of 3-Dimensional Geometry
- 3-Dimensional Geometry Master File
- 3-Dimensional Geometry Revision Notes
- 3-Dimensional Geometry Formulae
- 3-Dimensional Geometry Reference Book
- 3-Dimensional Geometry Past Many Years Questions and Answer
Examples and Exercise
IIT JEE (Main) Mathematics ,”3-Dimensional Geometry” Notes ,Test Papers, Sample Papers, Past Years Papers , NCERT , S. L. Loney and Hall & Knight Solutions and Help from Ex- IITian
About this unit
Coordinates of a point in space, the distance between two points. Section formula, direction ratios and direction cosines, the angle between two intersecting lines Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines.
IITian Academy Notes for IIT JEE (Main) Mathematics – 3-Dimensional Geometry
The success mantra of the JEE is practice and hard work. Gone are the days when students used to spend hours in attempting one question. Now it is an era of multiple choice questions. The JEE Mathematics questions test a student’s acquired knowledge as well as his aptitude. We have excellent notes prepared by Ex-IITian to best match the requirement of the exam.Focus is given on problem solving skills and small tips and tricks to do it faster and easier. We , Ex-IITian at https://www.iitianacademy.com. will make sure you understand the concept well.
IIT JEE (Main) Mathematics, 3-Dimensional Geometry Solved Examples and Practice Papers.
Get excellent practice papers and Solved examples to grasp the concept and check for speed and make you ready for big day. These Question Papers are prepared by Ex-IITIan for IIT JEE (Main) Mathematics , 3-Dimensional Geometry.
S. L. Loney IIT JEE (Main) Mathematics
This book is the one of the most beautifully written book by the author. Trigonometry is considered to be one of the easiest topics in mathematics by the aspirants of IIT JEE, AIEEE and other state level engineering examination preparation. It would not be untrue to say that most of the sources have taken inspiration from this book as it is the most reliable source. The best part of this book is its coverage in Heights and Distances and Inverse Trigonometric Functions. The book gives a very good learning experience and the exercises which follow are not only comprehensive but they have both basic and standard questions.. I will help you online for any doubt / clarification.
Hall & Knight IIT JEE (Main) Mathematics
Algebra by Hall and Knight is one of the best books for JEE preparation. Students preparing for IIT JEE and other engineering entrance exams as well as students appearing for board exams should read this everyday, especially to master Algebra and Probability. Hall and Knight have explained the concepts logically in their book.
IIT JEE (Main) Mathematics Assignments
Chapter wise assignments are being given by teachers to students to make them understand the chapter concepts. Its extremely critical for all CBSE students to practice all assignments which will help them in gaining better marks in examinations. All assignments available for free download on the website are developed by the best teachers having many years of teaching experience in CBSE schools all over the country. Students, teachers and parents are advised to contact me online incase of any doubt / clarification.
Past Many Years (40 Years) Questions IIT JEE (Main) Mathematics Solutions 3-Dimensional Geometry
Past 40 Years Question Papers Solutions for IIT JEE (Main) Mathematics 3-Dimensional Geometry are provided here with simple step-by-step explanations. These solutions for 3-Dimensional Geometry are extremely popular among IIT JEE (Main) students for Chemistry . 3-Dimensional Geometry Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Past Many Years Question Papers Book of IIT JEE (Main) Mathematics Chapter 3-Dimensional Geometry are provided here for . I will help you online for any doubt / clarification.