Sir, what will be the direction cosines of the line (x-2)/2=(2y-5)/-3 and z=4

The direction cosines of the line  are l, m and n.

Since we have z=4, the given line lies in the plane xy and it is perpendicular to the z axis.

 

Thus it makes an angle 90 degree with z axis.

 

Therefore the direction lines of the given line

 

 and z=4 are 2 , -3 and cos(90).

That is, the required direction cosines are 2, -3 and 0.