NCERT Class 12 · Ch 10 Miscellaneous Exercise · Q3
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Miscellaneous Exercise Question 3
A girl walks 4 km west, then 3 km at 30° east of north. Find her net displacement.
💡 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: (−5/2,3√3/2) km; magnitude √13 km, direction tan⁻¹(5/(3√3)) west of north.
- Take east as positive x, north as positive y. The first displacement is (−4,0); the second is (3sin30°,3cos30°)=(3/2,3√3/2).
- Add to get (−5/2,3√3/2), with magnitude √(25/4+27/4)=√13.
- It lies north-west; the angle west of north has tangent (5/2)/(3√3/2)=5/(3√3).
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