In $($Figure $1),$ F$=\{70$i$+30$j$+20$k$\}$lb

$.$

Figure$1$ of $1$

In the x y z space, a pole lying on the positive z axis is attached to a floor by its bottom end at the origin. Its free end $\text{'}$A$\text{'}$ is at $8$ feet from the origin. The pole is fastened to the floor by two cables, $\text{'}$A$\text{'}$ B and $\text{'}$A$\text{'}$ C$.$ Point B is in the x y plane $4$ feet from the positive x axis and $5$ feet from the negative y axis. Point C is in the x y plane, $4$ feet from the positive y axis and $3$ feet from the negative x axis. A force F acts at point $\text{'}$A$\text{'}.$

Part A

Determine the magnitude of the projection F

in the direction of the cable AB

$.$

Express your answer in pounds to three significant figures.

Activate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type

FAB

$=$

lb

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Part B

Determine the magnitude of the projection F

in the direction of the cable AC

$.$

Express your answer in pounds to three significant figures.

Activate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type

FAC

$=$

nothing