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GATE 2016 ME (ME3) – Question 9

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 2 marks · Multiple choice

M and N start at the same location. M travels 10 km east and then 10 km northeast. N travels 5 km south and then 4 km southeast. Their shortest separation at the end is ______ km.

  1. 18.60
  2. 22.50
  3. 20.61
  4. 25.00

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Show answer and explanation

Correct answer: (C) 20.61

Explanation

Take east as+x and north as+y. M ends at(10+10/√2,10/√2), and N at(4/√2,−5−4/√2). The displacement is(10+6/√2,5+14/√2), whose length is20.6118km. Hence **20.61km, C**; route lengths cannot simply be subtracted.