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## Homework Statement

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.

## 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?