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NDA 2024 Maths · Mathematics · Three Dimensional Geometry · medium

The perpendicular distance of the point (2,-3,6) from the x-axis is

Single correct option

The perpendicular distance of the point (2,−3,6)(2,-3,6) from the xx-axis is
  1. A. 77
  2. B. 353\sqrt5
  3. C. 13\sqrt{13}
  4. D. 2102\sqrt{10}
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Answer: (B) 353\sqrt5

The foot of the perpendicular on the xx-axis is (2,0,0)(2,0,0), so the distance is (−3)2+62=45=35\sqrt{(-3)^2+6^2}=\sqrt{45}=3\sqrt5. Trap: 7 is the distance from the origin, 13\sqrt{13} is the distance from the zz-axis (4+9\sqrt{4+9}), and 210=402\sqrt{10}=\sqrt{40} is the distance from the yy-axis.
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Original question written in the NDA 2024 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