Consider East as +ve x -axis, North as +ve y -axis. A girl walks 10 m East first time then 10 m in a direction 3 0 ∘ West of North for the 2 nd time \& then third time in unknown direction and magnitu

Question

Consider East as +ve x -axis, North as +ve y -axis. A girl walks 10 m East first time then 10 m in a direction 3 0 ∘ West of North for the 2 nd time \& then third time in unknown direction and magnitude, so as to return to her initial position. What is her third displacement vector :-

TestHub · Accepted Answer

The net displacement is zero. r 1 ​ = 10 i ^ , r 2 ​ = − 10 sin ( 3 0 ∘ ) i ^ + 10 cos ( 3 0 ∘ ) j ^ ​ = − 5 i ^ + 5 3 ​ j ^ ​ r 1 ​ + r 2 ​ + r 3 ​ = 0 ⟹ r 3 ​ = − ( r 1 ​ + r 2 ​ ) = − ( 5 i ^ + 5 3 ​ j ^ ​ ) = − 5 i ^ − 5 3 ​ j ^ ​ The third displacement vector is − 5 i ^ − 5 3 ​ j ^ ​ .

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