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Q.

Please give the solution for this question

If an angle between the line, \(\frac {x + 1}{2} = \frac {y - 2}{1} = \frac {z - 3}{-2}\) and the plane, \(x-2 y-\mathrm{k} z=3\)is \(\cos ^{-1}\left(\frac{2 \sqrt{2}}{3}\right)\), then a value of \(k\) is :

(a) \(\sqrt{\frac{5}{3}}\)

(b) \(\sqrt{\frac{3}{5}}\)

(c) \(-\frac{3}{5}\)

(d) \(-\frac{5}{3}\)