NCERT Solutions for Class 11 Maths Chapter 12 Miscellaneous Exercise Introduction to Three Dimensional Geometry in Hindi and English Medium. All the solutions are updated for CBSE and State board students’ academic session 2022-2023.

## NCERT Solutions for Class 11 Maths Chapter 12 Miscellaneous Exercise

### Important Questions of 11th Maths Miscellaneous Exercise 12

In the miscellaneous exercise of chapter 12it is suggested that students go through example 11 (wherein we are required to prove point A, B, C and D are vertices of a parallelogram not a rectangle). In a parallelogram all the sides may not be equal. Just prove that the opposite sides are equal. Don’t worry if the sides are rational or irrational. We should also prove that the diagonals AC and BD are unequal.

#### Examples of Chapter 12 Miscellaneous Exercise

All examples of miscellaneous exercises are important for exams. There are some tricky questions also based on concepts different from other exercises. A way of proving that ABCD is parallelogram is that diagonals AC and BD bisect each other. Example 12 – relates to finding out set of point B, such that it is equidistant from point A and B. in other words we are required to prove that PA is equal to PB.

##### Important Examples and their Solutions

In example 13 we have been given the coordinates of point A and B. We have to find coordinates of point C and the coordinates of centroid is given. A similar question (question 3) is given for practices where the origin is centroid. At the end, it is better to work out all examples and question because the exercise is not lengthy and more or less, it is in extension of what we have already studied in class 10. Before starting the exercise, must do all the examples.

###### Questions of Class 11 Maths Chapter 12 Miscellaneous Exercise

There are only 6 questions given in Class 11 Maths chapter 12 miscellaneous exercise. The first question is based on mid-point formula. In second question, we have to find the length of medium using distance formula.

The question number 3 is based on the concept of centroid. Questions 4 and 5 are based on distance formula and the last questions is little bit tricky to solve. Most of the questions are easy to understand.    