To understand Cartesian representations of vectors and how they can be determined from direction and magnitude; to learn how to represent vectors expressed as a product of the component magnitude and the unit direction vectors i

$,$ j

$,$ and k

; and to learn how to represent a vector component as a function of the angle between the vector and the coordinate axis.

As shown, a pole is subjected to three forces: F

$,$ P

$,$ and T

$.$ The force F

expressed in Cartesian vector form is F$=[8$ i$+8$ j$+8$ k$]$ N

$.$ Force P

has magnitude $7\mathrm{.}35$ N

and acts in the direction given by these direction angles: $\backslash$alpha $=114$

$,\backslash$beta $=35\mathrm{.}3$

$,$ and $\backslash$gamma $=65\mathrm{.}9$

to the x$,$ y$,$ and z axes, respectively. Force T

lies within the yz

plane, its direction is given by the $3-4-5$ triangle shown, and its magnitude is $16$ N

$.$