Question

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

Answer 1

The mutually perpendicular direction means that all the forces which are directed towards the point are in 90 degrees with each other that means that all the cosines of angle between them will not be there.

Complete step by step solution:
The general formula to calculate magnitude of a vector is given as:
$\left\| a \right\| = \sqrt {a_1^2 + a_2^2}$;
Here:
a = The net vector quantity.
${a_1}$= A vector quantity.
Here, we need to calculate the net force which is applied at a point in a particular direction. The net force is calculated by adding all the squares of the given forces together and then taking their root. Here, we have been given three forces 3N, 4N and 12N.
${F_{net}} = \sqrt {F_1^2 + F_2^2 + F_3^2}$ ;
Now, put in the given value in the above relation:
${F_{net}} = \sqrt {{3^2} + {4^2} + {{12}^2}}$;
Do the square of the digits and then take their root:
$\Rightarrow {F_{net}} = \sqrt {169}$;
The final value of the net applicable force is:
$\Rightarrow {F_{net}} = 13N$

Option B is the correct option. Therefore, if forces 3N,4N and 12N act at a point in mutually perpendicular directions then the magnitude of the resultant force would be 13N.

Note: The magnitude of a vector is also known as the length of the vector. Essentially a vector has both direction and magnitude and when we take its magnitude the direction doesn’t play a role and the calculated magnitude gives its length only.