Answer
$F_1 = 18.3\ lb$
$F_2 = 35.6\ lb$
Work Step by Step
To calculate the forces we must first know the value of:
$u_{OA} = \dfrac{3i + 5j - 3k}{\sqrt{3^2 + 5^2 + (-3)^2}} = \dfrac{3i + 5j - 3k}{\sqrt{43}}$
We proceed to calculate the forces:
$F_1 = F \cdot u_{OA} = (-40k) \cdot \left(\dfrac{3i + 5j -3k}{\sqrt{43}}\right) = 18.3\ lb$
$F_2 = \sqrt{F_2^2 - F_1^2} = \sqrt{40^2 - 18.3^2} = 35.6\ lb$
