Knowledge organisers

Introduction to Three Dimensional Geometry: CBSE Class 11 Maths knowledge organiser

Everything to know about introduction to three dimensional geometry on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Octant: One of the eight regions the three coordinate planes divide space into.
Coordinates in space: (x, y, z): signed distances from the yz-, zx- and xy-planes.
Distance in 3D: √((x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²).

Key formulas

Octants I–IV \(z>0\), V–VIII \(z<0\); on the \(x\)-axis \((x,0,0)\), in the \(xy\)-plane \((x,y,0)\)
\(PQ\)	\(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\)

Worked example

Find the distance between \((2, -1, 3)\) and \((-2, 1, 3)\).

\(\sqrt{16 + 4 + 0} = \sqrt{20} = 2\sqrt5\).

Common mistakes

Forgetting the \(z\) term in the distance formula.
Distance from the \(x\)-axis taken as \(|a|\): it is \(\sqrt{b^2 + c^2}\).
Confusing "on the \(x\)-axis" \((x, 0, 0)\) with "in the \(xy\)-plane" \((x, y, 0)\).
Claiming collinearity from two equal distances instead of \(AB + BC = AC\).

You should be able to…

Place points in octants and on axes and planes, and use the distance formula.
Find unknown coordinates from distances and test triangles and collinearity.
Classify quadrilaterals in space and handle loci with the distance formula.
Find distances from axes and loci of equidistant points.

The printable sheet

Introduction to Three Dimensional Geometry knowledge organiser for CBSE Class 11 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Introduction to Three Dimensional Geometry knowledge organiser (CBSE Class 11 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 11 Maths topics: Sets · Relations and Functions · Trigonometric Functions · Complex Numbers and Quadratic Equations · Linear Inequalities · Permutations and Combinations · Binomial Theorem · Sequences and Series · Straight Lines · Conic Sections · Limits and Derivatives · Statistics · Probability · All CBSE Class 11 Maths organisers