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Misc 3 - A girl walks 4 km west, then 3 km 30 east of north - Addition(resultant) of vectors

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Misc 3 A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure. Let initial point of departure be O(0, 0) & OA = 4km AB = 3km ∠ XAB = 30° We need to find OB Now, ∠ BAO = 90° – ∠ XAB = 90° – 30° = 60° Let us draw BD ⊥ OA Now, OD = OA – AD OD = 4 – 𝟑﷮𝟐﷯ = 𝟒 𝟐﷯ − 𝟑﷮𝟐﷯ = 𝟓﷮𝟐﷯ Now, In right triangle Δ BDO Hypotenuse2 = Base2 + Height2 OB2 = OD2 + BD2 OB2 = 5﷮2﷯﷯﷮2﷯+ 3 ﷮3﷯﷮2﷯﷯﷮2﷯ OB2 = 25﷮4﷯+ 3﷮2﷯ ﷮3﷯﷯﷮2﷯﷮ 2﷮2﷯﷯ OB2 = 25﷮4﷯+ 9 × 3﷮4﷯ OB2 = 25﷮4﷯+ 27﷮4﷯ OB2 = 52﷮4﷯ OB2 = 13 OB = ﷮13﷯ Therefore, the displacement of the girl from her initial point of departure is ﷮𝟏𝟑﷯ km.

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