A force of 10N act north and a force of 4N act south and a force of 8N act east find the magnitude.

if you mean the magnitude of the resultant, then since it is

<0,10> + <0,-4> + <8,0> = <8,6>
its magnitude is 10

Fr = 10i - 4i + 8 = 8 + 6i.

Fr = sqrt(8^2 + 6^2) = 10 N. = Resultant force.

To find the magnitude of the resultant force, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, the north and south forces are acting along the same direction, so we can simply subtract them to find the net force along that direction. The east force acts perpendicular to the north-south direction, so we can treat it as the other side of a right-angled triangle.

Using the Pythagorean theorem, the magnitude of the resultant force (R) can be calculated as follows:

R^2 = (10N - 4N)^2 + (8N)^2

R^2 = (6N)^2 + (8N)^2

R^2 = 36N^2 + 64N^2

R^2 = 100N^2

Taking the square root of both sides, we find:

R = 10N

Therefore, the magnitude of the resultant force is 10N.

To find the magnitude of the resulting force, we can use vector addition. We need to add the vectors representing the forces acting on the object.

First, let's represent the forces as vectors:

- The force acting north has a magnitude of 10N and is directed towards the north. We'll call this vector F_north.
- The force acting south has a magnitude of 4N and is directed towards the south. We'll call this vector F_south.
- The force acting east has a magnitude of 8N and is directed towards the east. We'll call this vector F_east.

Now, we can add these vectors together using vector addition.

To add vectors, we need to break them down into their x and y components. For example, the force acting north does not have an x-component, but it has a y-component of +10N. Similarly, the force acting south has a y-component of -4N, and the force acting east has an x-component of +8N.

Let's represent the x-component of the resulting force as Fx and the y-component as Fy.

Fx = 8N (east)
Fy = 10N (north) - 4N (south) = 6N (north)

Now, using these components, we can find the magnitude of the resulting force (F) using the Pythagorean theorem:

F = √(Fx² + Fy²)

Plugging in the values:

F = √((8N)² + (6N)²)
F = √(64N² + 36N²)
F = √(100N²)
F = 10N

Hence, the magnitude of the resulting force is 10N.