Force 3N, 4N and 12N act a point in mutually perpendicular directions. The magnitude of the resultant force is:A) 19NB) 13NC) 11ND) 5N

To find the magnitude of the resultant force when three forces of 3N, 4N, and 12N act at a point in mutually perpendicular directions, you can use the Pythagorean theorem for vectors.

The Pythagorean theorem states that the magnitude of the resultant vector (R) formed by adding two vectors (A and B) at right angles to each other is given by:

R^2 = A^2 + B^2

In this case, you have three perpendicular forces: 3N, 4N, and 12N.

First, find the magnitude of the resultant of the two forces in the plane formed by 3N and 4N:

R1^2 = (3N)^2 + (4N)^2
R1^2 = 9N^2 + 16N^2
R1^2 = 25N^2
R1 = 5N

Now, you have the magnitude of the resultant force in the plane formed by 3N and 4N, which is 5N.

Next, find the magnitude of the resultant force when you add the third force, 12N, perpendicular to the plane of the first two forces:

R^2 = R1^2 + (12N)^2
R^2 = (5N)^2 + 144N^2
R^2 = 25N^2 + 144N^2
R^2 = 169N^2
R = √(169N^2)
R = 13N

So, the magnitude of the resultant force is 13N, which is option (B).