Question 2.159: The pole supporting the sign is parallel to the x axis and i......
The pole supporting the sign is parallel to the x axis and is 6 ft long. Point A is contained in the y –z plane. (a) Express the vector r in terms of components. (b) What are the direction cosines of r?
The pole supporting the sign is parallel to the x-axis.
The length of the pole is 6 ft.
Point A is contained in the y-z plane.
Final Answer
The vector r is
r =| r |\left(\sin 45^{\circ} i +\cos 45^{\circ} \sin 60^{\circ} j +\cos 45^{\circ} \cos 60^{\circ} k \right)
The length of the pole is the x component of r. Therefore
| r | \sin 45^{\circ}=6~ft \Rightarrow| r |=\frac{6~ft }{\sin 45^{\circ}}=8.49~ft
(a) r = (6.00i + 5.20j + 3.00k) ft
(b) The direction cosines are
\cos \theta_x=\frac{r_x}{| r |}=0.707, \cos \theta_y=\frac{r_y}{| r |}=0.612, \cos \theta_z=\frac{r_z}{| r |}=0.354
\cos \theta_x=0.707, \cos \theta_y=0.612, \cos \theta_z=0.354