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NDA 2016 Maths · Mathematics · Three Dimensional Geometry · medium

The planes 2x+3y-z=5 and 4x+6y-2z=7 are perpendicular. 2. The lines with direction ratios (1,2,3) and (1,1,-1) are perpendicular.

Single correct option

Consider the following statements:
1. The planes 2x+3y−z=52x+3y-z=5 and 4x+6y−2z=74x+6y-2z=7 are perpendicular.
2. The lines with direction ratios (1,2,3)(1,2,3) and (1,1,−1)(1,1,-1) are perpendicular.
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (B) 2 only

The normals (2,3,−1)(2,3,-1) and (4,6,−2)(4,6,-2) are proportional, so the planes are parallel, not perpendicular; statement 1 is false. For the lines, 1+2−3=01+2-3=0, so they are perpendicular and statement 2 is true.
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Original question written in the NDA 2016 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