The force F acts through the origin. What is the magnitude of F and what angles does it make with x,y,z axes? F = 2.63i + 4.28j-5.92k N

To determine the magnitude of a force, we'll apply the
formula:

|F| = sqrt(a^2 + b^2 +
c^2)

where a,b,c are the coefficients of the unit vectors
i,j,k.

We'll identify the coefficients:
a,b,c.

F = 2.63i + 4.28j-5.92k
N

a = 2.63

b =
4.28

c = -5.92

|F| =
sqrt[(2.63)^2 + (4.28)^2 + (-5.92)^2]

|F| =
7.75 N

The angle that F makes with x axis
is:

cos theta x = a/|F|

cos
theta x = 2.63 / 7.75

cos theta x = 70.2
degrees

The angle that F makes with y axis
is:

cos theta y = b/|F|

cos
theta y = 4.28/7.75

cos theta y = 56.3
degrees

The angle that F makes with z axis
is:

cos theta z = c/|F|

cos
theta z =  -5.92/7.75

cos theta z = 139.8
degrees