Final answer:
The component of the force vector G along the force vector H is 3.8 N.
Step-by-step explanation:
To find the component of the force vector G along the force vector H, we can use the dot product formula:
G · H = |G| |H| cos θ
where |G| and |H| are the magnitudes of the vectors G and H, and θ is the angle between them.
Since H does not have a z-component, we can write it as H = (1.0ˆi + 4.0ˆj + 0.0ˆk)N.
Taking the dot product of G and H, we get G · H = (3.0)(1.0) + (4.0)(4.0) + (10.0)(0.0) = 3.0 + 16.0 = 19.0.
The component of G along H is then given by |G| cos θ = |G| (G · H / |G| |H|) = |G| (19.0 / (|(3.0)(1.0) + (4.0)(4.0) + (10.0)(0.0)|)) = 19.0 / √(9.0 + 16.0) = 19.0 / √25.0 = 19.0 / 5.0 = 3.8 N.
Therefore, the component of the force vector G along the force vector H is 3.8 N.