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## QuestionMathsClass 12

lf the equations $$2{x}-{k}{y}+5z=7$$ and $$kx-8y-10z+14=0$$ represents the same plane then $$k^{2}-k+1=$$

(A) $$4$$
(B) $$12$$
(C) $$21$$
(D) $$0$$

The given equations are $$2x-ky+5z=7$$ and $$kx-8y-10z+14=0$$.
If the two equations represent the same plane, the ratio of the coefficients should remain a constant.
$$\dfrac{2}{k} =\dfrac{-k}{-8} =\dfrac{5}{-10} =\dfrac{7}{-14}$$
i.e. $$k = -4$$
Substituting in the required expression,
$${k}^{2} - k + 1 = 16 + 4 + 1 = 21$$