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NCERT Solutions Class 12 Maths Chapter 11 Three-dimensional Geometry is concisely made by the mentors of the subject matter. We provide NCERT Solutions to make it easy for students to learn and revise all different concepts. NCERT Solutions Class 12 has in-depth solutions to important concepts.

  • Three Dimensional Geometry – 3D geometry has mathematical shapes in 3D space which also involves all 3 coordination. We have three different coordinates which work together namely \(x\)-coordination, \(y\)-coordination, and \(z\)-coordination. In 3d geometry, we can find the location of any point in the space with the help of other coordination. In the application of 3 d geometry, we can perfectly find out location and position.
  • Rectangular coordinate system – when three lines are mutually perpendicular to each other. The common point of all three axes meets at the origin.  
  • Distance from the origin – the distance between origin and any particular point is found by the Pythagoras theorem. The distance of \(P(x,y,z)\) from origin \((0,0,0)\) is \(\sqrt {x^2 + y^2 + z^2}\)
  •  Distance between two different points in space - Distance between 2 points  \(P(x_1+y_1+z_1)\) and \(Q(x_2+y_2+z_2)\) is \(\sqrt {(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\) 
  • Division of the line joining 2 points - Let \(P(x_1,y_1,z_1)\) and \(Q(x_2,y_2,z_2)\) be \(2\) points. R derives the line segment PQ in ratio internally. Then R has coordinate \({mx_2+nx_1 \over m+n},{my_2+ny_1 \over m+n},{mz_2+nz_1 \over m+n}\)
  • Direction Cosines and Direction Ratios of a Line – the direction ratio of a line are calculated with the help of a number proportional to the direction cosine. The direction numbers are represented with symbols such as \(a,b,\) and \(c\). at the unit level the sum of the square of the direction cosines is \(1\).
  • Equation of a Line in Space – whenever we make a line on a graphical plane it has a slope which is represented by \(m\). the equation of a line is represented by \(y = mx + c.\)

Our expert team at Sarthaks has made NCERT Solutions Class 12 Maths for students’ complete understanding of different concepts for easy learning and understanding of all kinds of topics.

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