Introduction to Three Dimensional Geometry — Class 11 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Introduction to Three Dimensional Geometry" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Introduction to Three Dimensional Geometry" — 8 important questions with detailed…
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Key Questions Covered:
- Find the distance between the points A(1, 2, 3) and B(4, 5, 6) in 3D space.
- Find the coordinates of the point that divides the line segment joining A(2, …
- Find the direction cosines of the line joining the points A(2, 3, 1) and B(6,…
- + 5 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Find the distance between the points A(1, 2, 3) and B(4, … | ✓ Solved |
| Find the coordinates of the point that divides the line s… | ✓ Solved |
| Find the direction cosines of the line joining the points… | ✓ Solved |
Showing 3 of 8 questions
Q1: Find the distance between the points A(1, 2, 3) and B(4, 5, 6) in 3D space.
Given points: A(1, 2, 3) and B(4, 5, 6)
Step 1: Use the distance formula in 3D:
d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
Step 2: Substitute the coordinates:
d = √[(4 - 1)² + (5 - 2)² + (6 - 3)²]
d = √[3² + 3² + 3²]
d = √[9 + 9 + 9]
d = √27
d = 3√3
Step 3: Simplify:
d = 3√3 ≈ 5.196 units
Final...
Q2: Find the coordinates of the point that divides the line segment joining A(2, 3, 4) and B(8, 9, 10) in the ratio 1:2 internally.
Given: A(2, 3, 4), B(8, 9, 10), and ratio m:n = 1:2
Step 1: Use the section formula for internal division:
P = [(m × x₂ + n × x₁)/(m + n), (m × y₂ + n × y₁)/(m + n), (m × z₂ + n × z₁)/(m + n)]
Step 2: Substitute m = 1, n = 2:
P = [(1 × 8 + 2 × 2)/(1 + 2), (1 × 9 + 2 × 3)/(1 + 2), (1 × 10 + 2 × 4)/...
Q3: Find the direction cosines of the line joining the points A(2, 3, 1) and B(6, 9, 7).
Given points: A(2, 3, 1) and B(6, 9, 7)
Step 1: Find the direction ratios:
Direction ratios = (6 - 2, 9 - 3, 7 - 1) = (4, 6, 6)
Step 2: Find the magnitude of direction ratios:
|d| = √(4² + 6² + 6²)
|d| = √(16 + 36 + 36)
|d| = √88
|d| = 2√22
Step 3: Find direction cosines by dividing each ratio by...
Showing 3 of 8 questions. Visit the full page for complete solutions.