Answer:
Option A
Explanation:
Given point be (2,3,\lambda) and equation of the plane be
r.(3\hat{i}+2\hat{j}+6\hat{k})=13
\therefore (x\hat{i}+y\hat{j}+z\hat{k}).(3\hat{i}+2\hat{j}+6\hat{k})=13
[\because r.(x\hat{i}+y\hat{j}+z\hat{k})]
\Rightarrow 3x+2y+6z=13
or 3x+2y+6z-13=0
Now, distance of the plane from the point (2,3, \lambda)
d=|\frac{ax_{1}+by_{1}+cz_{1}+d}{\sqrt{a^{2}+b^{2}+c^{2}}}|
5=|\frac{3\times2+2\times3+6 \times\lambda-13}{\sqrt{3^{2}+2^{2}+6^{2}}}|
[given , d=5]
\pm5=\frac{6+6+6 \times\lambda-13}{\sqrt{9+4+36}}
\Rightarrow \pm5=\frac{6\lambda-1}{\sqrt{49}}
\therefore 5=|\frac{6\lambda-1}{7}|
\Rightarrow \pm35=6\lambda-1
\Rightarrow 35=6\lambda-1
or -35=6\lambda-1
\Rightarrow \lambda=6,\lambda=-\frac{17}{3}