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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2018 · Mathematics · Three Dimensional Geometry

Consider the following statements: 1. The angle between the planes...

Consider the following statements: 1. The angle between the planes 2x−y+z=1 and x+y+2z=3 is π32.Thedistancebetweentheplanes6x−3y+6z+2=0 and 2x−y+2z+4=0 is 1092 x-y+z=1 \text{ and } x+y+2 z=3 \text{ is } \frac{\pi}{3} 2. The distance between the planes 6 x-3 y+6 z+2=0 \text{ and } 2 x-y+2 z+4=0 \text{ is } \frac{10}{9} Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth and 2
  4. DNeither 1 nor 2

Correct answer

C. Both and 2

Step-by-step solution

Angle between planes =cos⁡−1(2−1+26)=cos⁡−1(12)=π3\begin{aligned} & =\cos ^{-1}\left(\frac{2-1+2}{6}\right) \\ & =\cos ^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{3} \end{aligned} Distance between planes =∣23−4∣9=103×3=109=\frac{\left|\frac{2}{3}-4\right|}{\sqrt{9}}=\frac{10}{3 \times 3}=\frac{10}{9}
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