More practice questions

4. Q4. A person walks 4 km due east and then 6 km at 60° north of east. Find the resultant displacement.

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   x: 4 + 6 cos 60° = 7 km; y: 6 sin 60° ≈ 5.20 km. R = √(49 + 27) = √76 ≈ 8.72 km, at tan^⁻¹(5.20/7) ≈ 36.6° north of east.

5. Q5. Find C such that A + B + C = 0, for A = 2î − 3ĵ and B = −5î + ĵ.

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   C = −(A + B) = −(−3î − 2ĵ) = 3î + 2ĵ.

6. Q6. Two vectors have magnitudes 6 and 8 units and the angle between them is 60°. Find |A + B| and |A − B|.

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   |A + B| = √(36 + 64 + 48) = √148 ≈ 12.2 units. |A − B| = √(36 + 64 − 48) = √52 ≈ 7.21 units.