Part A $-$ Moment due to a force specified by magnitude and endpoints

As shown, a member is fixed at the origin, point $O,$ and has an applied force $F,$ the tension in the rope, applied at the free end, point $B.($Figure $1)$

The force has magnitude $F=160N$ and is directed as shown. The dimensions are $x_1=0\mathrm{.}350m,x_2=1\mathrm{.}80m,y_1=2\mathrm{.}60m,$ and $z_1=1\mathrm{.}10m.$

What is the moment about the origin due to the applied force $F?$

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$i,j,k$

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Learning Goal:

To use the vector cross product to calculate the moment produced by a force, or forces, about a specified point on a member.

The moment of a force $F$ about the moment axis passing through $O$ and perpendicular to the plane containing O and $F$ can be expressed using the vector cross product, $M_O=rF.$ In a properly constructed Cartesian coordinate system, the vector cross product can be calculated using a matrix determinant: $$

$M=rF=|[i,j,k],[r_x,r_y,r_z],[F_x,F_y,F_z]|$

Notice that the order of the elements of the matrix determinant is important; switching rows $2$ and $3$ of the determinant would change the sign of the moment from positive to negative $($or vice versa.$)$

Figure

$1$ of $3$