The pipe shown in Figure $2$ is fixed at end $A,$ which is centered on the origin and

can rotate around that point. A force, $F_B,$ is applied at end B $,$ of $F_B=-10i+$

$20j+30k$ Newtons. All dimensions are in metres.

Figure $2-$ Diagram of a set of pipes, fixed at point $A,$ to which a force is applied at point $B.$

a$.$ Determine the position vector of point $B$ relative to point $A$

b$.$ Using the cross$-$product, obtain the determinant matrix expression for the

moment that $F_B$ creates about the fixed end at $A$

c$.$ Will the determinant expression $($part b$)$ result in a vector or a scalar result?

Explain the meaning of the terms in the resulting expression

d$.$ To determine the moment about an arbitrary axis $($call it $w)$ other than $x,y,$ or

$z$ axes, the top row of the determinant can be changed to the coefficients of

the unit vector which defines the direction of the arbitrary w axis.

Using MATLAB and showing your command used, determine the moment

about a line running through point A which has unit vector $-0\mathrm{.}37i+0\mathrm{.}56j+$

$0\mathrm{.}74$ k

e$.$ What is the angle between the applied force and the line described in part d$?$