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NDA 2019 Maths · Mathematics · Three Dimensional Geometry · medium

The planes ax+by+cz=d1 and ax+by+cz=d2 with d1≠ d2 are parallel. 2. Two lines with direction ratios (1,2,3) and (2,4,6) must be the same line.

Single correct option

Consider the following statements:
1. The planes ax+by+cz=d1ax+by+cz=d_1 and ax+by+cz=d2ax+by+cz=d_2 with d1≠d2d_1\ne d_2 are parallel.
2. Two lines with direction ratios (1,2,3)(1,2,3) and (2,4,6)(2,4,6) must be the same line.
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: (A) 1 only

Both planes have the same normal (a,b,c)(a,b,c), and with d1≠d2d_1\ne d_2 they do not coincide, so they are parallel; statement 1 is true. Proportional direction ratios show only that the lines are parallel; they may be distinct parallel lines passing through different points, so statement 2 is false. Only statement 1 is correct.
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Original question written in the NDA 2019 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