Vector Algebra — Class 12 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Vector Algebra" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Vector Algebra" — 8 important questions with detailed answers for CBSE board exam…
By Syllab.in · Updated
Key Questions Covered:
- Find the magnitude of the vector a = 3î + 4ĵ.
- Find the dot product of vectors a = 2î + 3ĵ + k̂ and b = î + 2ĵ - k̂.
- Find the cross product a × b where a = î + 2ĵ + 3k̂ and b = 2î + 3ĵ + k̂.
- + 5 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Find the magnitude of the vector a = 3î + 4ĵ. | ✓ Solved |
| Find the dot product of vectors a = 2î + 3ĵ + k̂ and b = … | ✓ Solved |
| Find the cross product a × b where a = î + 2ĵ + 3k̂ and b… | ✓ Solved |
Showing 3 of 8 questions
Q1: Find the magnitude of the vector a = 3î + 4ĵ.
To find the magnitude of a = 3î + 4ĵ:
Step 1: Use the magnitude formula.
For a vector a = xî + yĵ + zk̂,
|a| = √(x² + y² + z²)
Step 2: Identify components.
Here: x = 3, y = 4, z = 0
Step 3: Calculate.
|a| = √(3² + 4² + 0²)
= √(9 + 16)
= √25
= 5
Final Answer: |a| = 5 units
Q2: Find the dot product of vectors a = 2î + 3ĵ + k̂ and b = î + 2ĵ - k̂.
To find a · b where a = 2î + 3ĵ + k̂ and b = î + 2ĵ - k̂:
Step 1: Use dot product formula.
a · b = (a₁î + a₂ĵ + a₃k̂) · (b₁î + b₂ĵ + b₃k̂)
= a₁b₁ + a₂b₂ + a₃b₃
Step 2: Identify components.
a₁ = 2, a₂ = 3, a₃ = 1
b₁ = 1, b₂ = 2, b₃ = -1
Step 3: Calculate.
a · b = (2)(1) + (3)(2) + (1)(-1)
= 2 + 6 ...
Q3: Find the cross product a × b where a = î + 2ĵ + 3k̂ and b = 2î + 3ĵ + k̂.
To find a × b where a = î + 2ĵ + 3k̂ and b = 2î + 3ĵ + k̂:
Step 1: Use the determinant formula.
a × b = |î ĵ k̂ |
|1 2 3 |
|2 3 1 |
Step 2: Expand the determinant.
a × b = î(2×1 - 3×3) - ĵ(1×1 - 3×2) + k̂(1×3 - 2×2)
= î(2 - 9) - ĵ(1 - 6) + k̂(3 - 4)
= î(-7) - ĵ...
Showing 3 of 8 questions. Visit the full page for complete solutions.