find the magnitude resultant of two forces (3j+4j) and (3j+4k)

Those are the same force! I assume a typo.

if you have a resultant Xi + Yj + Kk, the magnitude is
sqrt(x^2+y^2 + k^2)

Sqroot74 =ans

To find the magnitude of the resultant force of two forces, you need to add the two forces vectorially and then calculate the magnitude of the resulting vector.

Given the two forces:
Force 1 = 3j + 4j
Force 2 = 3j + 4k

To add the forces vectorially, we can add their corresponding components:

Force 1 = (0i + 3j + 0k) + (0i + 4j + 0k) = 0i + 7j + 0k
Force 2 = (0i + 3j + 0k) + (0i + 0j + 4k) = 0i + 3j + 4k

Now, add the forces together:

Resultant Force = Force 1 + Force 2
= (0i + 7j + 0k) + (0i + 3j + 4k)
= 0i + 10j + 4k

To calculate the magnitude of the resultant force, we use the formula:

Magnitude (Resultant Force) = sqrt((x^2) + (y^2) + (z^2))

where x, y, and z are the components of the resultant force.

Magnitude (Resultant Force) = sqrt((0^2) + (10^2) + (4^2))
= sqrt(0 + 100 + 16)
= sqrt(116)
≈ 10.77

Therefore, the magnitude of the resultant force is approximately 10.77 units.