GATE AG 2015 • Q13 NAT • 1 Mark

Section 3: Farm Power

Farm Power

Subtopic: Thermodynamic principles of I.C. engines

Question Statement:

The distance PQ between two position vectors ⃗P = −2î+3ĵ+4k̂ and ⃗Q = 4î+5ĵ+7k̂ is _____.

Official Answer Key:

7

Step-by-Step Solution & Explanation

⃗PQ = ⃗Q − ⃗P = (4−(−2))î + (5−3)ĵ + (7−4)k̂ = 6î + 2ĵ + 3k̂. |⃗PQ| = √(6²+2²+3²) = √(36+4+9) = √49 = 7. Matches the official key exactly.

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