There are 3 vectors of 1N , 2N and 3N which form an equilateral triang

1.	There are 3 vectors of 1N , 2N and 3N which form an equilateral triangle. Find their resultant vector.
Answer» Ans 0............... can you please explain why ? The three forces will be along three directions separated by 120 deg. from each other drawn at a point P. Let them be PA of 1 N. PB = 2 N and then PC = 3 N.. Let us draw PA horizontally along positive x axis.PB is at 30 deg. anticlockwise from + y axis.PC will be at 30 deg. clockwise from - y axis... Resolving components along x axis and adding: = 1 N + 2 N * Cos 120 + 3 N * Cos 240 = 1 - 2 * 1/2 - 3 /2= - 3/2 Newtons Resolving components along y axis and adding = 0 N + 2 N √3 /2 - 3 N √3/2 = -√3/2 Newtons So resultant is R = -1.5 i -√3 /2 j where i and j are unit vectors. magnitude = √[ 1.5² + 3/4 ] =√3 Newtons. The three vectors form closed triangle, so the resultant is 0.

There are 3 vectors of 1N , 2N and 3N which form an equilateral triangle. Find their resultant vector.

Answer»

Ans 0...............

can you please explain why ?

The three forces will be along three directions separated by 120 deg. from each other drawn at a point P. Let them be PA of 1 N. PB = 2 N and then PC = 3 N..

Let us draw PA horizontally along positive x axis.PB is at 30 deg. anticlockwise from + y axis.PC will be at 30 deg. clockwise from - y axis... Resolving components along x axis and adding: = 1 N + 2 N * Cos 120 + 3 N * Cos 240 = 1 - 2 * 1/2 - 3 /2= - 3/2 Newtons Resolving components along y axis and adding = 0 N + 2 N *√3 /2 - 3 N *√3/2 = -√3/2 Newtons

So resultant is R = -1.5 i -√3 /2 j where i and j are unit vectors. magnitude = √[ 1.5² + 3/4 ] =√3 Newtons.

The three vectors form closed triangle, so the resultant is 0.

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