If the angles made by the normal of the plane $2x+3y-4z-16=0$ with the coordinates axes X, Y, Z are , then $Co{s}^{-1}{k}_1,Co{s}^{-1}{k}_2,Co{s}^{-1}{k}_3$ respectively are

The d.r’s of normal of the plane $2x+3y-4z-16=0$ are $\left(2,3,-4\right)$ and the d.c’s are  $\left(\frac{{\displaystyle 2}}{{\displaystyle \sqrt{29}}},\frac{{\displaystyle 3}}{{\displaystyle \sqrt{29}}},\frac{{\displaystyle -4}}{{\displaystyle \sqrt{29}}}\right)$
$\therefore \cos \alpha =\frac{2}{\sqrt{29}},\cos \beta =\frac{3}{\sqrt{29}},\cos \gamma =\frac{-4}{\sqrt{29}}$
Where $\alpha ,\beta ,\gamma$ are the angle made by the normal with X, Y, Z axes respectiely.
$\therefore \alpha =Co{s}^{-1}\left(\frac{{\displaystyle 2}}{{\displaystyle \sqrt{29}}}\right),\beta =Co{s}^{-1}\left(\frac{{\displaystyle 3}}{{\displaystyle \sqrt{29}}}\right)$
$\gamma =Co{s}^{-1}\left(\frac{{\displaystyle -4}}{{\displaystyle \sqrt{29}}}\right)$
 $\therefore k_1,k_2,k_3$ values are  $\frac{2}{\sqrt{29}},\frac{3}{\sqrt{29}},\frac{-4}{\sqrt{29}}$ respectively