# NCERT Solutions for Class 12 Maths Chapter 11

NCERT Solutions for Class 12 Maths Chapter 11 Three dimensional geometry (3D) Exercise 11.1, 11.2, 11.3 & Miscellaneous exercises in PDF form to free download updated for new academic session 2020-21.

NCERT solutions, Sample question papers, Assignments, test papers based on different difficulty levels, latest CBSE syllabus for the current academic year 2020-2021. Join the Discussion Forum and ask your doubts.## NCERT Solutions for Class 12 Maths Chapter 11

Class: | 12 |

Subject: | Maths |

Chapter 11: | Three dimensional geometry |

### 12th Maths Chapter 11 Solutions

NCERT Solutions for Class 12 Maths Chapter 11 are given below to download in PDF form free. Join the discussion forum to ask your doubts related to NIOS board and CBSE board. Download latest NCERT Books 2020-2021 following the current CBSE Syllabus.

### Chapter 11 Solutions in PDF

- Download Exercise 11.1 in PDF
- Download Exercise 11.2 in PDF
- Download Exercise 11.3 in PDF
- Download Miscellaneous Exercise 11
- NCERT Book Chapter 11
- NCERT Book Answers
- Revision Book Chapter 11
- Revision Book Answers
- Download Assignment 1
- Download Assignment 2
- Download Assignment 2 Answers
- Download Assignment 3
- Download Assignment 4
- Visit to 12th Maths Main Page

#### Previous Years Important Questions

1. Find the Cartesian and Vector equations of the line which passes through the point (-2, 4, -5) and parallel to the line given by (x+3)/3 = (y-4)/5 = (8-z)/-6. [CBSE Sample Paper 2017]

2. If the vectors p = ai + j + k, q = i + bj + k and r = i + j + ck are co-planar, then for a, b, c ≠ 1, show that 1/(1-a) + 1/(1-b) + 1/(1-c) = 1. [CBSE Sample Paper 2017]

3. A plane meets the coordinate axes in A, B and C such that the centroid of triangle ABC is the point (α, β, γ). Show that the equation of the plane is x/α + y/β + z/γ = 3. [CBSE Sample Paper 2017]

4. Define skew lines. Using only vector approach, find the shortest distance between the following two skew lines: r = (8 + 3m)i – (9 + 16m)j + (10 + 7m)k and r = 15i + 29j + 5k + n(3i + 8j – 5k). [CBSE Sample Paper 2017]

5. Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line 5x – 25 = 14 – 7y = 35z. [Delhi 2017]

##### Questions from Board Papers

1. Find the vector and Cartesian equations of a line passing through (1, 2, –4) and perpendicular to the two lines (x – 8)/3 = (y + 19)/-16 = (z – 10)/7 and (x – 15)/3 = (y – 29)/8 = (z – 5)/-5. [Delhi 2017]

2. Find the vector equation of a plane which is at a distance of 5 units from the origin and its normal vector is 2i – 3j + 6k. [Delhi 2016]

3. Show that the vectors a, b, and c are co-planar if a + b + c and c + a are co-planar. [Delhi 2016]

4. Find the coordinate of the point P where the line through A(3, – 4, –5) and B (2, –3, 1) crosses the plane passing through three points L(2, 2, 1), M(3, 0, 1) and N(4, –1, 0). Also, find the ratio in which P divides the line segment AB. [Delhi 2016]

5. Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x – y + z = 0. Then find the distance of plane thus obtained from the point A(1, 3, 6). [Delhi 2015C]