2 30 points Refer to Figure 2 A tension force of magnitude T

2. (30 points) Refer to Figure 2. A tension force of magnitude T = 50 N acts at A. Represent the force T as a Cartesian vector and determine its coordinate direction angles.

Solution

Here, the length of the segment AB is

r = sqrt(4^2+12^2+6^2) = 14

Here, we see that, if alpha, beta, and gamma are the direction angles of T, then

cos alpha = -4/14 --> alpha = 106.6 deg
cos beta = 12/14 --> beta = 31.0 deg
cos gamma = 6/14 --> gamma = 64.62 deg [DIRECTION ANGLES, ANSWER]

Thus, as a cartesion vector,

T = <50(-4/14), 50(12/14), 50(6/14)>

T = <-14.286, 42.857, 21.429> N [ANSWER]