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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2010 · Mathematics · Three Dimensional Geometry

If the line through the points A(k, 1,-1) and B(2 k, 0,2) is...

If the line through the points A(k,1,−1)\mathrm{A}(k, 1,-1) and B(2k,0,2)\mathrm{B}(2 k, 0,2) is perpendicular to the line through the points BB and C(2+2k,k,1)\mathrm{C}(2+2 k, k, 1), then what is the value of kk ?

Options

  1. A-1
  2. B1
  3. C-3
  4. D3

Correct answer

D. 3

Step-by-step solution

AB=(2k−k,0−1,2+1)=(k,−1,3)BC=(2+2k−2k,k−0,1−2)=(2,k,−1)k×2−1×k−3=0⇒2k−k=⇒k=3\begin{aligned} \mathrm{AB}=(2 k-k & , 0-1,2+1) \\ & =(k,-1,3) \\ \mathrm{BC} & =(2+2 k-2 k, k-0,1-2) \\ & =(2, k,-1) \\ k \times 2-1 \times k & -3=0 \\ \Rightarrow 2 k-k= & \Rightarrow k=3\end{aligned}
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