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NDA 2025 Maths · Mathematics · Three Dimensional Geometry · medium

The lines with direction ratios (1,2,2) and (2,k,-3) are perpendicular if k is equal to

Single correct option

The lines with direction ratios (1,2,2)(1,2,2) and (2,k,−3)(2,k,-3) are perpendicular if kk is equal to
  1. A. 22
  2. B. −2-2
  3. C. 44
  4. D. −1-1
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Answer: (A) 22

Two lines are perpendicular when a1a2+b1b2+c1c2=0a_1a_2+b_1b_2+c_1c_2=0. Here 1⋅2+2k+2⋅(−3)=01\cdot2+2k+2\cdot(-3)=0, so 2k=42k=4 and k=2k=2. The value −2-2 comes from a sign error in 2−62-6, 44 from forgetting to divide by the coefficient 22, and −1-1 from dropping a term. Verify by substituting back.
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Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake