A point object is acted upon by forces of 4N, 5N and 6N is in equilibrium. IF=f the 6N force is removed, what is the resultant force on the object now?

I really want to know how tow find relationship between 3 forces, and is there anything to do with cos rule??? HELPPPPP-.-

sorry i don't no,,,,

i m so sorry because i don't know

If three force vectors add to zero, they must be co-planer. This means that any one of them is the equilibrium of the other two. Therefore, when one is removed, the other two add to give the negative of the one that was removed. In this case, the 4N force and the 5N force add to give the negative of the 6N force that was removed.

To find the resultant force on the object, we need to understand the concept of vector addition. We can use the graphical method or the component method to add the forces together.

Graphical Method:
1. Draw a vector diagram to scale, representing each force.
2. Place the tail of each force vector at the origin of the coordinate system.
3. Starting from the tail of the first force vector, draw the subsequent force vectors one after another in a consistent direction.
4. Connect the tail of the first vector with the tip of the last vector to form the resultant vector.
5. Measure the magnitude and direction of the resultant vector.

Component Method (using the cosine rule):
1. Resolve each force vector into its horizontal and vertical components.
2. Add up the horizontal components and vertical components separately.
3. Use the Pythagorean theorem to find the magnitude of the resultant vector: Magnitude of Resultant Force = sqrt(sum of (horizontal components)^2 + sum of (vertical components)^2)
4. Use inverse trigonometry (arctan) to find the angle of the resultant vector: Angle of Resultant Force = arctan(sum of (vertical components) / sum of (horizontal components))

In this specific case:
Let's assume the forces of 4N, 5N, and 6N act along the positive x-axis, positive y-axis, and an angle of θ with respect to the positive x-axis, respectively.

Using the component method:
1. The horizontal components are 4N and -6N (resolved by taking the cosine of the angle θ).
2. The vertical components are 5N and 0N (resolved by taking the sine of the angle θ).
3. Summing up the horizontal components: 4N - 6N = -2N.
4. Summing up the vertical components: 5N + 0N = 5N.
5. Magnitude of Resultant Force = sqrt((-2N)^2 + (5N)^2) ≈ 5.39N (rounded to two decimal places).
6. Angle of Resultant Force = arctan(5N / -2N) = -68.2° (rounded to one decimal place).

So, the resultant force on the object, after the 6N force is removed, is approximately 5.39N in magnitude and at an angle of -68.2° with respect to the positive x-axis.