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NDA 2021 Maths · Mathematics · Three Dimensional Geometry · medium

For the line (x-1)/(2)=(y+1)/(3)=(z-2)/(6), the direction cosine with respect to the z-axis is

Single correct option

For the line x−12=y+13=z−26\dfrac{x-1}{2}=\dfrac{y+1}{3}=\dfrac{z-2}{6}, the direction cosine with respect to the zz-axis is
  1. A. 16\dfrac16
  2. B. 67\dfrac67
  3. C. 611\dfrac{6}{\sqrt{11}}
  4. D. 37\dfrac37
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Answer: (B) 67\dfrac67

The direction ratios (2,3,6)(2,3,6) have magnitude 4+9+36=7\sqrt{4+9+36}=7, so the direction cosines are (27,37,67)\left(\tfrac27,\tfrac37,\tfrac67\right). The zz-direction cosine is 6/76/7; the point (1,−1,2)(1,-1,2) does not affect it.
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Original question written in the NDA 2021 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