Express the 5.2-kN force F as a vector in terms of the unit vectors i, j, and k. Determine the scalar projections of F onto the x-axis and onto the line OA.
I have attached an image of the problem.
Fx = Fcos(θ)
Fy = Fcos(θ)
Fz = Fcos(θ)
The Attempt at a Solution
Firstly I tried to find the unit vector nxy
nxy = sin(4)i + cos(4)j
Then I tried to find the unit vector of F:
nF = cos(41)nxy + sin(41)k
nF = cos(41)[sin(4)i + cos(4)j] + sin(41)k
n = cos(41)sin(4)i + cos(41)cos(4)j + sin(41)k
Then F = F°nF (dot product)
F = 5.2[cos(41)sin(4)i + cos(41)cos(4) + sin(41)k]
F = 0.2738i + 3.9149j + 3.412 k
I checked that this was true by squaring i, j and k, adding them together and then squaring the result.
sqrt(0.2738^2 +3.9149^2 + 3.412^2)) = 5.20 kN
However, it says that only my value for K is correct.
With the projection of F onto OA I used the dot product, whereby:
F = 0.2738i + 3.9149j + 3.412k
n)A = cos(33)i + sin(33)j
F°nOA = (0.2738*cos(33))i + (3.9149*sin(33))j + 3.142k*0
F°nOA = 0.2296 + 2.132
= 2.36187 kN
Unsurprisingly this was wrong too.
Any suggestion for where I'm going wrong?