Physics vector question?

Question

vector A = 5 meters at 25 degrees

vector B = 8 meters at 60 degrees

If vectors A + B described a walking path from some arbitrary starting point, how far and in what direction would you have to walk to return to the exact starting point along the shortest path possible?

Answer 1

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Sum the components:

Dx:

5* Cos(25)+ 8* Cos(60) =8.53153893518323 m

Dy:

5* Sin(25)+ 8* Sin(60) =9.04129453897902 m

With rounding:How far:

Sqrt(Dx^2+Dy^2) = 12.4311 m

Arctan(Dy/Dx) = 46.66 degrees

Direction to starting point:

Angle = 180+46.66 = 226.66 degrees CCW

Answer 2

A = 5m @ 25°

B = 8m @ 60°

The X component of A is 5·Cos(25°)

The X component of B is 8·Cos(60°)

Add the X components together to find the X component of the answer.

The Y component of A is 5·Sin(25°)

The Y component of B is 8·Sin(60°)

Add the Y components together to find the Y component of the answer.

The distance of the answer is √(final Y component² + final X component²).

The angle of the answer is Arctan(final Y component/final X component).