Force 4n,3n and 12n act at a in point mutually perpendicular directions .The magnitude of resultant force is
step by step do
[sqrt(16+9)]^2 = 5
sqrt(25+144) = sqrt(169) =13
or simply sqrt (16+9+144)
To find the magnitude of the resultant force, we need to use the concept of vector addition. This involves adding the individual force vectors together to obtain the resultant vector.
Given that the forces are acting at mutually perpendicular directions, we can think of them as the components of a single resultant vector. In this case, we have forces of 4N, 3N, and 12N acting along the x, y, and z axis respectively.
To find the magnitude of the resultant force, we can use the Pythagorean theorem in three dimensions. It states that the magnitude of a vector (r) can be calculated using the scalar components (Rx, Ry, and Rz) as follows:
r = sqrt(Rx^2 + Ry^2 + Rz^2)
In this case, we have the following components:
Rx = 4N
Ry = 3N
Rz = 12N
Applying the formula, we get:
r = sqrt(4N^2 + 3N^2 + 12N^2)
= sqrt(16N^2 + 9N^2 + 144N^2)
= sqrt(169N^2)
= 13N
Therefore, the magnitude of the resultant force is 13N.