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NDA 2020 Maths · Mathematics · Three Dimensional Geometry · easy

The distance of the point (3,-4,12) from the z-axis is

Single correct option

The distance of the point (3,−4,12)(3,-4,12) from the zz-axis is
  1. A. 55
  2. B. 1313
  3. C. 1212
  4. D. 77
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Answer: (A) 55

The foot of the perpendicular from (x,y,z)(x,y,z) to the z-axis is (0,0,z)(0,0,z), so the distance is x2+y2=9+16=5\sqrt{x^2+y^2}=\sqrt{9+16}=5. The value 1313 is the distance from the origin, 9+16+144\sqrt{9+16+144}, and 1212 is the distance from the xy-plane. The value 77 results from adding 3+43+4 without squaring. For the x-axis the distance would be y2+z2\sqrt{y^2+z^2}.
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Original question written in the NDA 2020 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