Aforce is specified by the vector f = (105i + 135j - 175k) n. calculate the angles made by f with the positive x-, y-, and z-axes.

Calculate the direction cosines, and hence find the angles.

unit vector
=<105,135,-175>/sqrt(105^2+135^2+(-175)^2)
=<21/sqrt(2395),27/sqrt(2395),-35/sqrt(2395)>
=<0.4291,0.5517,-0.7152> (approx.)

Therefore the direction cosines are respectively
0.4291,0.5517,-0.7152, and the angles with the x,y and z-axes are:
acos(0.4291),acos(0.5517),acos(-0.7152)
=64.59, 56.51, and 135.66 degrees respectively.