Answer:
The value is [tex]\vec F_{n} = -5.67 i +14.82 j \ \ N[/tex]
Explanation:
From the question we are told that
The magnitude of the first force is [tex]F_1 = 20 \ N[/tex]
The angle which it makes with the x-axis is [tex]\theta_1 = 120 ^o[/tex]
The magnitude of the second force is [tex]F_2 = 5 \ N[/tex]
The angle which it make with x-axis is [tex]\theta_2 = -30 ^o[/tex]
Generally the x-component of the first force is
[tex]F__{1x}} = 20 cos (120 )[/tex]'
=> [tex]F__{1x}} = -10 \ N[/tex]
Generally the y-component of the first force is
[tex]F__{1y}} = 20 sin (120 )[/tex]
=> [tex]F__{1y}} = 17.32 \ N[/tex]
Generally the vector representation of the first force is mathematically represented as
[tex]\vec F_1 = [ -10 i + 17.32 j \ ] \ N[/tex]
Generally the x-component of the second force is
[tex]F__{2x}} = 20 cos (-30 )[/tex]
=> [tex]F__{2x}} = 4.33 \ N[/tex]
Generally the y-component of the second force is
[tex]F__{2y}} = 20 sin (-30 )[/tex]
=> [tex]F__{2y}} = -2.5 \ N[/tex]
Generally the vector representation of the first force is mathematically represented as
[tex]\vec F_2 = [ 4.33 i - 2.5 j \ ] \ N[/tex]
Generally the net force acting that point is mathematically represented as
[tex]\vec F_{n} = -10 i + 17.32 j + 4.33 i - 2.5 j[/tex]
=> [tex]\vec F_{n} = -5.67 i +14.82 j \ \ N[/tex]
