# Introduction to Three Dimensional Geometry Notes | SwaVid Introduction to Three Dimensional Geometry, NCERT Class 11 Mathematics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers. Canonical: https://www.swavid.com/cbse/class-11/maths/chapter/introduction-to-three-dimensional-geometry Source: https://www.swavid.com/cbse/class-11/maths/chapter/introduction-to-three-dimensional-geometry # Introduction to Three Dimensional Geometry ## Formulas and definitions ## Key ideas ## Common mistakes ## Quick checks ## Keep going ## Questions parents ask ## Class 11 Mathematics on SwaVid ### Coordinate axes and planes ### Coordinates of a point ### The eight octants ### Distance between two points ### Next chapter ### Related chapter ### Related chapter ### All chapters SwaVid › CBSE › Class 11 › Mathematics › Introduction to Three Dimensional Geometry Notes written by SwaVid from the NCERT textbook. Class 11 Mathematics, Chapter 11. Key ideas, formulas and common mistakes. CBSE does not print marks for a single chapter. Short answer. This chapter extends two-dimensional coordinate geometry into three-dimensional space by introducing three mutually perpendicular coordinate axes and planes. Students learn how to locate points across eight octants and compute distances between them using the three-dimensional distance formula. Source: NCERT Mathematics (Reprint 2026-27) , Chapter 11, Introduction to Three Dimensional Geometry Three mutually perpendicular lines intersecting at a common point called the origin form the x-axis, y-axis, and z-axis. These three axes taken in pairs determine three coordinate planes: the xy-plane, yz-plane, and zx-plane. Any point P in space is represented as an ordered triplet (x, y, z), which correspond to the directed distances from the yz-plane, zx-plane, and xy-plane respectively. A point on the x-axis has coordinates (x, 0, 0), on the y-axis (0, y, 0), and on the z-axis (0, 0, z). The three coordinate planes divide space into eight regions called octants. The sign of each coordinate depends on whether the point lies along the positive or negative direction of the respective axis. The distance between two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) is given by the square root of the sum of the squares of the differences of their corresponding coordinates. This is a direct extension of Pythagoras theorem to three dimensions. Try each question first. Then tap it to see the answer. Identify the signs of the coordinates: x is negative, y is positive, and z is negative. Compare with standard octant signs: (-, +, +) is octant II, so (-, +, -) is octant VI. Octant VI Apply the distance formula: PQ = √((-4 - 1)² + (1 - (-3))² + (2 - 4)²) Simplify the terms: PQ = √((-5)² + (4)² + (-2)²) Compute the sum: PQ = √(25 + 16 + 4) = √45 = 3√5 3√5 units AB = √((1 - (-2))² + (2 - 3)² + (3 - 5)²) = √(9 + 1 + 4) = √14 BC = √((7 - 1)² + (0 - 2)² + (-1 - 3)²) = √(36 + 4 + 16) = √56 = 2√14 AC = √((7 - (-2))² + (0 - 3)² + (-1 - 5)²) = √(81 + 9 + 36) = √126 = 3√14 Check collinearity: AB + BC = √14 + 2√14 = 3√14 = AC Collinear Limits and Derivatives . Straight Lines . Conic Sections . The 14 chapters of Class 11 Mathematics . The CBSE Class 11 Maths curriculum says it gives no chapter or unit-wise weightage. Theory is 80 marks, plus 20 for internal assessment. No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed. Limits and Derivatives. SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works. - Ch 11 NCERT book - 80 marks, theory paper - 3 quick checks - Assigning octant numbers incorrectly based on two-dimensional quadrants . Remember that octants I to IV have z positive and match the 2D signs of x and y, whereas octants V to VIII have z negative with the same sequence of x and y signs. - Assuming coordinates on coordinate planes have only one non-zero coordinate . Points on coordinate planes have only one coordinate equal to zero, such as (x, y, 0) on the xy-plane. A point with two zero coordinates lies on an axis, not merely on a plane. - Dropping minus signs inside squared differences in the distance formula . Write out (x₂ - x₁)² carefully with parentheses when coordinates are negative, noting that (x₂ - (-x₁)) becomes (x₂ + x₁). ## Key Links - [CBSE](https://www.swavid.com/cbse) - [Class 11](https://www.swavid.com/cbse/class-11) - [Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup) - [All 14 chapters](https://www.swavid.com/cbse/class-11/maths/chapters) - [NCERT Mathematics (Reprint 2026-27)](https://ncert.nic.in/textbook.php) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/limits-and-derivatives) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/straight-lines) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/conic-sections) - [Class 11 Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup)