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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2022 · Mathematics · Three Dimensional Geometry

A plane cuts intercepts 2,2,1 on the coordinate axes. What are the...

A plane cuts intercepts 2,2,1 on the coordinate axes. What are the direction cosines of the normal to the plane?

Options

  1. A<2/3,2/3,1/3⟩< 2 / 3,2 / 3,1 / 3\rangle
  2. B<1/3,2/3,2/3⟩< 1 / 3,2 / 3,2 / 3\rangle
  3. C⟨16,16,26⟩\left\langle\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}\right\rangle
  4. D⟨26,16,16⟩\left\langle\frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}\right\rangle

Correct answer

C. ⟨16,16,26⟩\left\langle\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}\right\rangle

Step-by-step solution

Equation plane is x2+y2+z1=1⇒x+y+2z−2=0∴\frac{x}{2}+\frac{y}{2}+\frac{z}{1}=1\Rightarrow x+y+2 z-2=0\therefore direction ratio's of normal are ⟨1,1,2⟩\langle 1,1,2\rangle So, Direction cosines of normal are ⟨16,16,26⟩\left\langle\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}\right\rangle
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