Are these Introduction to Three Dimensional Geometry notes free?

Yes. The full 3-page Introduction to Three Dimensional Geometry sheet is free inside CapCompass, which runs in your browser with no account needed.

What does the Introduction to Three Dimensional Geometry revision sheet cover?

Three mutually perpendicular axes, The eight octants, Reading a point off its signs, (+,+,+), (-,+,+), (+,-,-), (0,0,z), Distance between two points, P(x_1,y_1,z_1) and Q(x_2,y_2,z_2), distance from the origin, Distance, built from a simpler idea, Worked: distance between two points in space.

Is this for Class 11 CBSE Mathematics?

It is written from the NCERT syllabus, so it serves CBSE and any board that follows NCERT for Mathematics.

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Introduction to Three Dimensional Geometry — Class 11 CBSE Mathematics revision notes

A 3-page visual revision sheet for Introduction to Three Dimensional Geometry, written for Class 11 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

Introduction to Three Dimensional Geometry revision notes, page 1 of 3 — A preview of page 1 — all 3 pages open full size in the app.

Introduction to Three Dimensional Geometry in one look

one more axis, one more squared term, same two ideas

Three mutually perpendicular axes

space needs three coordinate axes, x, y, z, mutually perpendicular, meeting at origin O
the three coordinate planes are XY (where z=0), YZ (where x=0) and ZX (where y=0)
a point in space is the triple (x,y,z): signed perpendicular distances from the three planes
the origin is (0,0,0); a point on the x-axis has y=0 and z=0 both

The eight octants

three coordinate planes cut space into 8 octants, as two axes cut a plane into 4
each octant is fixed by the SIGN of x,y,z: (+,+,+) is the first, (-,-,-) the opposite
swapping the sign of even one coordinate moves a point into a different octant

Reading a point off its signs

(+,+,+): first octant, all three coordinates positive
(-,+,+): y and z stay positive, only x flips
(+,-,-): only x stays positive
(0,0,z): not an octant at all, this sits ON the z-axis itself

Distance between two points

P(x_1,y_1,z_1) and Q(x_2,y_2,z_2) PQ=√(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2
distance from the origin OP=√x_1^2+y_1^2+z_1^2

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What this Introduction to Three Dimensional Geometry sheet covers

Three mutually perpendicular axes
The eight octants
Reading a point off its signs
(+,+,+)
(-,+,+)
(+,-,-)
(0,0,z)
Distance between two points
P(x_1,y_1,z_1) and Q(x_2,y_2,z_2)
distance from the origin
Distance, built from a simpler idea
Worked: distance between two points in space
Then the z step, added the same way
Section formula, dividing a segment
internal division, ratio m:n, P between A(x_1,y_1,z_1) and B(x_2,y_2,z_2)
external division, m≠ n
midpoint, the special case m=n
centroid of a triangle with vertices (x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)
Section formula: the special ratios
Internal vs external division
Internal
External
Worked: point dividing a segment in a given ratio
Symbols
Traps that cost marks
Tricks that save time

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