please help! find magnitude and direction (the counterclockwise angle with the +x axis) of a vector that is equal to a + c

Option (2)

Explanation:

From the figure attached,

Horizontal component,

     = 7.22 m

Vertical component,

    = 9.58 m

Similarly, Horizontal component of vector C,

 = C[Cos(60)]

     = 6[Cos(60)]

     =

     = 3 m

    = 5.20 m

Resultant Horizontal component of the vectors A + C,

m

= 4.38 m

Now magnitude of the resultant will be,

From ΔOBC,

   =

   =

   = 6.1 m

Direction of the resultant will be towards vector A.

tan(∠COB) =

                  =

                  =

m∠COB =

             = 46°

Therefore, magnitude of the resultant vector will be 6.1 m and direction will be 46°.

Option (2) will be the answer.