Given the force F = 3.5i + 3.5j - 7k N determine the magnitude of the force and the angles with axis . F passes through origin .

We have the force F defined as F = 3.5i + 3.5j - 7k
N

Now we need to find the magnitude and the angle that the
vector F makes with the axes.

For a vector F= ai + bj +
ck

The magnitude |F| is given by sqrt(a^2 + b^2 +
c^2)

=> sqrt [(3.5)^2 + (3.5)^2 +
(-7)^2]

=> 8.57 N

|F| =
8.57 N

The angle that F makes with x axis is given by a/
|F|

=> cos x = 3.5/
8.57

=> cos x =
0.4084

=> x = arccos (0.4084) = 65.89
degrees

The angle that F makes with the y axis is given by
b/|F|

=> cos y = 3.5/
8.57

=> cos y =
0.4084

=> y = arccos
(0.4084)

=> y = 65.89
degrees

The angle that F makes with the z axis is given by
c/|F|

=> cos z
=  -7/8.57

=> cos z
= -0.8168

=> z = arccos ( -0.8168) = 35.23
degrees

Therefore the magnitude of F is 8.57
N and teh angles made with the x, y and z axes is 65.89, 65.89,  and 35.23 degrees
respectively