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Homework Statement
Express the 5.2kN force F as a vector in terms of the unit vectors i, j, and k. Determine the scalar projections of F onto the xaxis and onto the line OA.
I have attached an image of the problem.
Homework Equations
F_{x} = Fcos(θ)
F_{y} = Fcos(θ)
F_{z} = Fcos(θ)
The Attempt at a Solution
Firstly I tried to find the unit vector n_{xy}
n_{xy} = sin(4)i + cos(4)j
Then I tried to find the unit vector of F:
n_{F} = cos(41)n_{xy} + sin(41)k
which becomes:
n_{F} = 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°n_{F} (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°n_{OA} = (0.2738*cos(33))i + (3.9149*sin(33))j + 3.142k*0
F°n_{OA} = 0.2296 + 2.132
= 2.36187 kN
Unsurprisingly this was wrong too.
Any suggestion for where I'm going wrong?
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