Using the position vector from $A$ to $C,$ calculate the moment about segment $AB$ due to force $F.$

Express the individual components to three significant figures, if necessary, separated by commas.

Learning Goal:

To gain insight into the independence of the scalar triple product from the point on the line chosen as the reference point of the calculation.

The general process $($not referenced to Figure $1)$ to calculate the moment of a force about a specified axis is as follows:

The magnitude of a moment about a line segment connecting points $P$ and $Q$ due to a force $F$ applied at point $R($with $R$ not on the line through $P$ and $Q)$ can be calculated using the scalar triple product,

$M_{PQ}=u_{PQ}*rF,$

where $r$ is a position vector from any point on the line through $P$ and $Q$ to $R$ and $u_{PQ}$ is the unit vector in the direction of line segment $PQ.$ The unit vector $u_{PQ}$ is then multiplied by this magnitude to find the vector representation of the moment.

As shown in the figure, the member is anchored at A and section $AB$ lies in the $x-y$ plane. The dimensions are $x_1=1\mathrm{.}4m,y_1=1\mathrm{.}8m,$ and $z_1=1\mathrm{.}5m.$ The force applied at point $C$ is

$F=|$~$-185i+150i+190k$~$|N.$

Figure

$1$ of $1$

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Part C $-$ Calculating the moment about $AB$ using the position vector $BC$

Using the position vector from $B$ to $C,$ calculate the moment about segment $AB$ due to force $F.$

Express the individual components to three significant figures, if necessary, separated by commas.

View Available Hint$($s$)$

$i,j,k$

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