NCERT Class 12 · Ch 10 Exercise 10.4 · Q3
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.4 Question 3
A unit vector makes angles π/3 with i, π/4 with j and acute θ with k. Find θ and its components.
💡 Concept Hints
- Write the vector components and identify the required direction or geometric relation.
- Use the magnitude, dot-product, cross-product or section formula that matches the requested quantity.
✅ Step-by-Step Solution
Final Answer: θ=π/3; components (1/2,1/√2,1/2).
- The direction cosines l=1/2, m=1/√2 obey l²+m²+n²=1, so n²=1−1/4−1/2=1/4.
- Since θ is acute, n=1/2 and θ=π/3. Components of a unit vector equal its direction cosines.
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