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

NDA 2022 · Mathematics · Three Dimensional Geometry

The plane 6 x+k y+3 z-12=0 where meets the coordinate axes at A, B...

The plane 6x+ky+3z−12=06 x+k y+3 z-12=0 where meets the coordinate axes at A,BA, B and CC respectively. The equation of the sphere passing through the origin and A,B,CA, B, C is x2+y2+z2−2x−3y−4z=0x^2+y^2+z^2-2 x-3 y-4 z=0. What is the value of kk ?

Options

  1. A3
  2. B4
  3. C6
  4. D12

Correct answer

B. 4

Step-by-step solution

Since B(0,12k,0)B\left(0, \frac{12}{k}, 0\right) lies on sphere ∴0+(12k)2+0−0−3(12k)0=0⇒(12k)[12k−3]=0\begin{aligned} & \therefore 0+\left(\frac{12}{\mathrm{k}}\right)^2+0-0-3\left(\frac{12}{\mathrm{k}}\right) 0=0 \\ & \Rightarrow\left(\frac{12}{\mathrm{k}}\right)\left[\frac{12}{\mathrm{k}}-3\right]=0\end{aligned} ⇒12k−3=0[∵k≠0]⇒k=4\begin{aligned} & \Rightarrow \frac{12}{\mathrm{k}}-3=0[\because \mathrm{k} \neq 0] \\ & \Rightarrow \mathrm{k}=4\end{aligned}
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