NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry Ex 12.3 are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry Ex 12.3.

- Introduction to Three Dimensional Geometry Class 11 Ex 12.1
- Introduction to Three Dimensional Geometry Class 11 Ex 12.2

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 11 |

Subject |
Maths |

Chapter |
Chapter 12 |

Chapter Name |
Introduction to Three Dimensional Geometry |

Exercise |
Ex 12.3 |

Number of Questions Solved |
5 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry Ex 12.3

**Ex 12.3 Class 11 Maths Question 1.**

Find the coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) in the ratio

**(i)** 2 : 3 internally,

**(ii)** 2 : 3 enternally

**Solution:**

**(i)** Let P(x, y, z) be any point which divides the line segment joining the points A(-2, 3, 5) and B(1, -4, 6) in the ratio 2 : 3 internally.

**(ii)** Let P(x, y, z) be any point which divides the line segment joining the points 71 (-2, 3, 5) and B(1, -4, 6) in the ratio 2 : 3 externally. Then

**Ex 12.3 Class 11 Maths Question 2.**

Given that P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) are collinear. Find the ratio in which Q divides PR.

**Solution:**

Let Q(5, 4, -6) divides the line segment joining the points P(3, 2, -4) and R(9, 8, -10) in the ratio k : 1 internally.

**Ex 12.3 Class 11 Maths Question 3.**

Find the ratio in which the YZ-plane divides the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8).

**Solution:**

Let the line segment joining the points A(-2, 4, 7) and B(3, -5, 8) be divided by the YZ -plane at a point C in the ratio k : 1.

**Ex 12.3 Class 11 Maths Question 4.**

Using section formula, show that the points A(2, -3, 4), B(-1, 2, 1) and C\(\left( 0,\frac { 1 }{ 3 } ,2 \right) \) are collinear.

**Solution:**

Let the points A(2, -3, 4), B(-l, 2,1) and C\(\left( 0,\frac { 1 }{ 3 } ,2 \right) \) be the given points. Let the point P divides AB in the ratio k : 1. Then coordinates of P are \(\left( \frac { -k+2 }{ k+1 } ,\frac { 2k-3 }{ k+1 } ,\frac { k+4 }{ k+1 } \right) \)

Let us examine whether for some value of k, the point P coincides with point C.

AB internally in the ratio 2:1. Hence A, B, C are collinear.

**Ex 12.3 Class 11 Maths Question 5.**

Find the coordinates of the points which trisect the line segment joining the points P(4, 2, -6) and Q(10, -16, 6).

**Solution:**

Let R and S be two points which trisect the line segment PQ.

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