NCERT Solutions for Class 11 Mathematics Introduction To Three Dimensional Geometry Chapter 11
NCERT solutions for Class 11 Mathematics Chapter Introduction to Three Dimensional Geometry – complete answers & explanations
Class 11 Mathematics Chapter Introduction to Three Dimensional Geometry helps students understand how to represent and locate points in space using three coordinates. This chapter builds a strong base for spatial understanding, which is important for higher-level mathematics and real-life applications like physics and engineering. Students learn about coordinate axes, planes, octants, and distance between points in three-dimensional space. This blog provides clear and reliable NCERT solutions that help students check their answers and improve accuracy. Download the worksheet and practice alongside solutions for better clarity. Book a free trial now to get expert guidance and strengthen your understanding with the right approach.
NCERT Solutions for Class 11 Mathematics Introduction To Three Dimensional Geometry Chapter 11
What this NCERT chapter covers?
1. Understanding three mutually perpendicular coordinate
axes in space
2. Learning about coordinate planes like XY-plane, YZ-plane, and ZX-plane
3. Identifying the position of a point using ordered triplets (x, y, z)
4. Understanding octants and how signs of coordinates determine position
5. Learning how to locate a point in three-dimensional space
6. Applying the distance formula between two points in space
7. Verifying collinearity of points using distance relationships
8. Identifying geometric shapes like triangles and parallelograms using coordinates
9. Forming equations based on distance conditions
10. Strengthening algebraic and spatial reasoning skills for exams
How to use these NCERT solutions?
1. First read each question carefully and try solving it on your own
2. Use proper formulas like distance formula step by step
3. After attempting, compare your answers with the given NCERT solutions
4. Identify mistakes in calculations or concepts and correct them
5. Revise important formulas and concepts while checking answers
6. Parents and teachers can guide students in understanding each step
7. Follow the same order of questions as given in the worksheet
8. Use these solutions regularly for revision and exam preparation
Important tips & tricks for students
1. Always check the signs of coordinates before identifying octants
2. Memorize the distance formula and apply it carefully
3. Avoid calculation mistakes while squaring numbers
4. Write steps clearly to match NCERT answer presentation
5. Practice identifying coordinate planes and axes regularly
6. Revise concepts like collinearity and triangle properties
7. Pay attention to algebraic simplification in equations
8. Double-check final answers before moving to the next question
NCERT solutions – complete answer key
Exercise 11.1
1
y-coordinate = 0
z-coordinate = 0
2
y-coordinate = 0
3
1. I octant
2. IV octant
3. V octant
4. V octant
5. VI octant
6. II octant
7. III octant
8. VII octant
4
1. XY-plane
2. (x, y, 0)
3. 8
Exercise 11.2
1
1. √20
2. √43
3. √104
4. √20
2
Points are collinear
3
1. Isosceles triangle
2. Right angled triangle
3. Parallelogram
4
x – 2z – 1 = 0
5
x² + y² + z² = 9
Miscellaneous Exercise
1
(1, –2, 8)
2
√52, √52, √52
3
a = –2
b = –1
c = 3
4
2x² + 2y² + 2z² – 4x – 14y + 4z = k² – 109
Why NCERT solutions help students?
NCERT solutions help students build strong conceptual clarity and improve problem-solving skills. They follow the exact exam pattern and ensure students understand the correct method of answering. Regular practice with these solutions increases confidence and helps students perform better in school exams and competitive tests.
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