Determine the magnitude of moment of force P 50 N about lin

Determine the magnitude of moment of force P = 50 N about line OC. 3, 600 N middot m 424 N middot m 1, 600 N midddot m 0

Solution

EASY WAY by vectorS;

HOW: find the coordinates of the points B,E these are ( 0,8,9 ) and (0,0,15) wrt the origin and axes given in the figure (origina t O and axes x,y,z). We aim to find the vector eqn of the force.

Coordinates of E ( 0,0,15)

vector eqn of line BE = ( 0,0,15)-(0,8,9) = ( 0,-8, 6)

Hence force along BE is P( BE) = P(0,-8,6)

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Vector eqn of line OC around which the moment is reqd

do the same way ( coords of C - coords of O) = (12,8,9)-(0,0,0) = (12,8,9)

The moment of Force along BE around line OC is FX OC ( vector cross product) and we want the component along OC so net salar moment is F X OC. OC where (dot) is the dot or scalar product

Finf BE X OC is ( 120i -72j -96k)

take scalar product with OC ( 120i-72j-96k). (12i +8j+9k) = 120*12-72*9-96*9 = 1440 -576- 864 =0

Answer is given, choose it.

Best!!