Given: equation of blane x – 2y + 3z = 17 points (–2,4,7) and (3,–5,8)

find: ratio in which plane divides the line.

Calculations: let m = k and n = 1

⇒  it is in the from $\left(\frac{{\mathrm{mx}}_2+{\mathrm{nx}}_1}{\mathrm{m}+\mathrm{n}},\frac{{\mathrm{my}}_2+{\mathrm{my}}_1}{\mathrm{m}+\mathrm{n}},\frac{{\mathrm{mz}}_2+{\mathrm{mz}}_1}{\mathrm{m}+\mathrm{n}}\right)$

and here

x₁ = –2, y₁ = 4, z₁ = 7

x₂ = 3, y₂ = 4, z₂ = 7

$\Rightarrow \frac{3\mathrm{k}-2}{\mathrm{k}+1},\frac{-5\mathrm{k}+4}{\mathrm{k}+1},\frac{8\mathrm{k}+7}{\mathrm{k}+1}$

Now putting these point on the equation of plane 

$\Rightarrow \frac{3\mathrm{k}-2}{\mathrm{k}+1}-2\frac{(-5\mathrm{k}+4)}{\mathrm{k}+1}+3\frac{(8\mathrm{k}+7)}{\mathrm{k}+1}=17$

⇒  3k – 2 + 10k – 8 + 24k + 21 = 17k + 17

⇒   20k = 6

$\Rightarrow \mathrm{k}=\frac{6}{20}$

$\Rightarrow \mathrm{k}=\frac{3}{10}$

∴   option C is correct.