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

NDA 2022 · Mathematics · Three Dimensional Geometry

Consider the points A(2,4,6), B(-2,-4,-2), C(4,6,4) and D(8,14,12)...

Consider the points A(2,4,6),B(−2,−4,−2),C(4,6,4)A(2,4,6), B(-2,-4,-2), C(4,6,4) and D(8,14,12)D(8,14,12). Which of the following statements is/ are correct? 1. The points are the vertices of a rectangle ABCDA B C D. 2. The mid-point of ACA C is the same as that of BDB D. Select the correct answer using the code given below :

Options

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

Correct answer

B. 2 only

Step-by-step solution

AC=(4−2)2+(6−4)2+(4−6)2=4+4+4=23BD=(8+2)2+(14+4)2+(12+2)2=2187\begin{aligned} & A C=\sqrt{(4-2)^2+(6-4)^2+(4-6)^2} \\ & =\sqrt{4+4+4}=2 \sqrt{3} \\ & B D=\sqrt{(8+2)^2+(14+4)^2+(12+2)^2} \\ & =2 \sqrt{187} \end{aligned}\because A C \neq B D(i.e.,Diagonalsarenotequal.)So,statementiswrong.Midpointof( i.e., Diagonals are not equal.) So, statement is wrong. Mid point ofA C=(3,5,5)isequaltomidpointofis equal to mid point ofB D=(3,5,5)$ So, statement 2 is correct
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