For the figure shown: a) Determine angle between cables AB and AC. b) Determine

Question

For the figure shown:

a) Determine angle between cables AB and AC.

b) Determine the projection of force FAB on the strut OA.

Express result as a Cartesian vector.

c) Determine the magnitude of the vector perpendicular

to the projection of FAC on the strut OA.

Express this result as a Cartesian vector

I ONLY NEED PART C SO DON'T BOTHER WITH A OR B

For the figure shown: Determine angle between cables AB and AC. Determine the projection of force FAB on the strut OA. Express result as a Cartesian vector. Determine the magnitude of the vector perpendicular to the projection of FAC on the strut OA. Express this result as a Cartesian vector

Explanation / Answer

so we want to find (FAB * AO) AO

so AO point in the direction -6ft j - 2 ft z

now we have to normalize

so divide by sqrt(6^2 + 2^2) = sqrt (36+4)=sqrt(40)=2*sqrt(10)

so AO= 1/sqrt(10) [ -3 j - 1 z]

now FAB points in the AB direction

AB points -3i -6j +2k

normalization is sqrt(3^2 +6^2 + 2^2) = sqrt( 9+36+4)=sqrt(49)=7

so FAB=70lb* 1/7 (-3i -6j +2k)

FAB= (-30i -60j + 20k) lb

so FAB*AO=(-30i -60j + 20k)*1/sqrt(10)[ -3 j - 1 z]=1/sqrt(10)[-60*-3+20*-1]=50.596

so (FAB*AO)(AO)= 1/sqrt(10) *(-3*50.596 j - 50.596 z)= -48 j -16 k

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