Class 11 Maths - GUJARAT
Introduction to Three Dimensional Geometry
The Chapter 'Introduction to Three Dimensional Geometry' in Class 11 Mathematics builds a bridge from familiar 2D Cartesian planes to the 3D space we live in. You will learn how to locate points using three mutually perpendicular axes (X, Y, and Z), determine the coordinates of points in space, and find distances between them. This chapter also introduces section formulas and coordinates of centroids of triangles and tetrahedrons in 3D. It serves as a fundamental stepping stone for calculus and vector algebra in Class 12, carrying significant weight in the Gujarat (GSEB) board examinations through short and descriptive questions.
Start Learning FreeKey Concepts
Coordinate Axes and Planes in 3D
Space is divided into eight octants by three mutually perpendicular planes called the XY, YZ, and ZX planes, intersecting at the origin (0,0,0).
Coordinates of a Point in Space
Any point P in 3D space is represented by an ordered triplet (x, y, z), representing perpendicular distances from the YZ, ZX, and XY planes respectively.
Distance Formula
The straight-line distance between two points P(x1, y1, z1) and Q(x2, y2, z2) in space is calculated using an extension of the Pythagorean theorem in 3D.
Section Formula
It helps find the coordinates of a point that divides the line segment joining two given points in a specific ratio, both internally and externally.
Midpoint and Centroid Formulas
Special cases of the section formula used to find the exact midpoint of a line segment and the centroid of a triangle formed by three points in 3D space.
Important Formulas
Board Exam Info
In the Gujarat (GSEB) Class 11 Mathematics examination, this chapter typically carries around 4 to 6 marks. Questions usually include 1-mark objective/MCQ questions identifying octants, 2-mark direct application sums of the distance formula, and 3-mark analytical problems based on the section formula or proving geometric shapes like collinearity and vertices of triangles.
Frequently Asked Questions
How do we identify which octant a point (x, y, z) lies in?
The signs of the x, y, and z coordinates determine the octant. For example, if all coordinates are positive (+, +, +), the point lies in Octant I.
Is the distance of a point P(x, y, z) from the origin easy to calculate?
Yes, it is a simplified version of the distance formula where the second point is the origin (0, 0, 0), giving the formula OP = sqrt(x^2 + y^2 + z^2).
What is the difference between internal and external division formulas?
In internal division, the dividing point lies on the line segment joining the two points (using '+' in the section formula). In external division, the point lies outside the segment extended (using '-' in the section formula).
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