Three Dimensional Geometry — Class 12 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Three Dimensional Geometry" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Three Dimensional Geometry" — 8 important questions with detailed answers for CBSE…
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Key Questions Covered:
- Find the distance of the point (1, 2, 3) from the origin.
- Find the equation of the plane passing through points A(1, 2, 3), B(2, 3, 4),…
- Find the foot of perpendicular from point P(1, 3, 2) to the plane x + 2y - z …
- + 5 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Find the distance of the point (1, 2, 3) from the origin. | ✓ Solved |
| Find the equation of the plane passing through points A(1… | ✓ Solved |
| Find the foot of perpendicular from point P(1, 3, 2) to t… | ✓ Solved |
Showing 3 of 8 questions
Q1: Find the distance of the point (1, 2, 3) from the origin.
To find the distance from P(1, 2, 3) to origin O(0, 0, 0):
Step 1: Use the distance formula.
For points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂):
d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]
Step 2: Substitute values.
Here: P(1, 2, 3) and O(0, 0, 0)
d = √[(0-1)² + (0-2)² + (0-3)²]
= √[1 + 4 + 9]
= √14
Final Answ...
Q2: Find the equation of the plane passing through points A(1, 2, 3), B(2, 3, 4), and C(3, 1, 2).
To find the equation of plane through A, B, C:
Step 1: Find vectors AB and AC.
AB = (2-1, 3-2, 4-3) = (1, 1, 1)
AC = (3-1, 1-2, 2-3) = (2, -1, -1)
Step 2: Find the normal vector n = AB × AC.
n = |î ĵ k̂ |
|1 1 1 |
|2 -1 -1 |
= î[1×(-1) - 1×(-1)] - ĵ[1×(-1) - 1×2] + k̂[1...
Q3: Find the foot of perpendicular from point P(1, 3, 2) to the plane x + 2y - z = 5.
To find the foot of perpendicular from P(1, 3, 2) to plane x + 2y - z = 5:
Step 1: Find the equation of the line perpendicular to the plane.
Normal to plane: n = (1, 2, -1)
Line through P parallel to n:
(x, y, z) = (1, 3, 2) + t(1, 2, -1)
x = 1 + t
y = 3 + 2t
z = 2 - t
Step 2: Find intersection wi...
Showing 3 of 8 questions. Visit the full page for complete solutions.