# Answer on Mechanics | Relativity Question for noor

Question #2805

A vector D = [ 30 cm , 50 degree ] and vector F = [ 45 cm , 150 degree ]

Use the graphic method to find the magnitude and direction of the sum R = D + F ?

Use the graphic method to find the magnitude and direction of the sum R = D + F ?

Expert's answer

In Cartesian coordinates

The magnitude of vector is

The same you can get depicting D as vector that originates at {0;0}, has length of 30 cm, angle between positive x direction is 50; and depicting F as vector that originates at {0;0}, has length of 45 cm, angle between positive x direction is 150

**D={ρ**

F={ρ

D+F = {13.3-39;23+45.5} = {-25.7;45.5}._{1}cosφ;ρ_{1}sinφ} = {30*cos50;30*sin50} = {13.3;23}.F={ρ

_{2}cosφ;ρ_{2}sinφ} = {45*cos150;45*sin150} = {-39;22.5}.D+F = {13.3-39;23+45.5} = {-25.7;45.5}.

The magnitude of vector is

**M = √(-25.7**^{2}+22.5^{2}) = 52.26 cm.The same you can get depicting D as vector that originates at {0;0}, has length of 30 cm, angle between positive x direction is 50; and depicting F as vector that originates at {0;0}, has length of 45 cm, angle between positive x direction is 150

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