Magnitude and angles of a force

[IHave]

Homework Statement

a force is given by F= 20i - 60j + 90k N. Find its magnitude and the angles it forms with the coordinate axis.

Homework Equations

F = magnitude of F times the unit vector
magnitude is square root (Fx squared + Fy squared + Fz squared)
and the unit vector can be written as (cos(theta)x)i + (cos(theta)y)j + (cos(theta)z)k
x for x component
y for y component
z for z component

to find the angle of the x component: inverse cosine of Fx/magnitude

The Attempt at a Solution

For the magnitude I got 110
for the angles with respect to x, y, z: 79.5, 123.1, 35.1

please tell me if i did something wrong! thanks

 

[rock.freak667]

That should be correct.

 

[PeterO]

Homework Statement

a force is given by F= 20i - 60j + 90k N. Find its magnitude and the angles it forms with the coordinate axis.

Homework Equations

F = magnitude of F times the unit vector
magnitude is square root (Fx squared + Fy squared + Fz squared)
and the unit vector can be written as (cos(theta)x)i + (cos(theta)y)j + (cos(theta)z)k
x for x component
y for y component
z for z component

to find the angle of the x component: inverse cosine of Fx/magnitude

The Attempt at a Solution

For the magnitude I got 110
for the angles with respect to x, y, z: 79.5, 123.1, 35.1

please tell me if i did something wrong! thanks

Agree. All looks good.

 

[Lobezno]

If a textbook or something gives a different answer, it's possible the angle is in another measurement, for example radians.

 

[rwisz]

Your solution looks correct. However, it would be helpful to provide more context or explanation for the solution, such as explaining the use of the unit vector and the inverse cosine function. Additionally, it would be helpful to provide the units for the angles, as angles are typically measured in degrees or radians. Overall, your solution shows a good understanding of vector components and their relationship to magnitude and angles.