By going through these CBSE Class 11 Maths Notes Chapter 12 Introduction to three Dimensional Geometry Class 11 Notes, students can recall all the concepts quickly.

## Introduction to three Dimensional Geometry Notes Class 11 Maths Chapter 12

Co-ordinates of a Point: The co-ordinates of a point are the distances from the origin of the feet of the perpendiculars from the point on the respective co-ordinate axes.

Distance Formula : The distance between the points (x_{1} y_{1}, z_{1}) and (x_{2}, y_{2}, z_{2}) is given by \(\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}+\left(z_{2}-z_{1}\right)^{2}}\). The distance of the point (x, y, z) from the origin is given by \(\sqrt{x^{2}+y^{2}+z^{2}}\)

Section Formulae: .

(i) Section formula for internal division :

If P(x_{1} y_{1}, z_{1}) and Q(x_{2}, y_{2}, z_{2}) are two points. Let R be a point on the line segment P and Q such that it divides the join of P and Q internally in the ratio m_{1} : m_{2}.

Then, the co-ordinates of R are

(ii) Section formula for external division :

If P(x_{1} y_{1}, z_{1}) and Q(x_{2}, y_{2}, z_{2}) are two points and let R be a

point on PQ produced dividing it

externally in the ratio m_{1} : m_{2}(m_{1} ≠ m_{2}). Then, the co-ordinates of Rare

Mid-Point : The mid-point of the line segment joining (x_{1} y_{1}, z_{1}) and (x_{2} y_{2}, z_{2}) is \(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}, \frac{z_{1}+z_{2}}{2}\right)\)

Centroid : Centroid of the triangle whose vertices are (x_{1} y_{1}, z_{1}), (x_{2} y_{2}, z_{2}) and (x_{3} y_{3}, z_{3}) is