Ch 11 extends coordinate geometry to three dimensions. Students learn about the three coordinate axes, eight octants, and formula for distance and section division in 3D space.
Three mutually perpendicular axes (x, y, z) divide space into 8 octants. A point P in space has coordinates (x, y, z). The coordinate planes are xy-plane (z=0), yz-plane (x=0), and xz-plane (y=0).
Distance between P(x₁,y₁,z₁) and Q(x₂,y₂,z₂) = √[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²]. Section formula: point dividing PQ in ratio m:n has coordinates ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n), (mz₂+nz₁)/(m+n)).
Download: https://ncert.nic.in/textbook/pdf/kemh111.pdf | Complete book: https://ncert.nic.in/textbook/pdf/kemh1ps.zip
There are 8 octants, determined by the signs of x, y, z coordinates. For example: (+,+,+) is the first octant, (−,+,+) is the second, and so on. This is analogous to 4 quadrants in 2D.
Book a Trial + Diagnostic session. Get a personalized Learning Path with clear milestones, tutor match, and a plan recommendation — all within 24 hours.
Book Trial + Diagnostic →