How do you add vectors? Add the vector <3,4> to the vector that goes 7 units at an angle of 2π/3.

The sum of the two vectors is the vector <-0.5 , 4+3.5 >

Step-by-step explanation:

The horizontal component (x) of a vector whose magnitude is b units and its direction is Ф° is b cos Ф

The vertical component (y) of a vector whose magnitude is b and its direction is Ф is b sin Ф

The vector is <b cos Ф , b sin Ф>

∵ The vector goes 7 units at an angle

- That means its magnitude is 7 and its direction is  

∴ x = 7 cos(   )

∴ y = 7 sin(   )

∵ cos(   ) =  

∵ sin(   ) =  

- Substitute them in x and y

∴ x = (7)( )

∴ x = -3.5

∴ y = (7)( )

∴ y = 3.5

∴ The vector is <-3.5 , 3.5>

Now lets add the vectors by adding xs and ys components

∵ <3 , 4> + <-3.5 , 3.5 > = <3 + -3.5 , 4 + 3.5 >

∴  <3 , 4> + <-3.5 , 3.5> = <-0.5 , 4+3.5 >

∴ The sum of the two vectors is the vector <-0.5 , 4+3.5 >

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step-by-step explanation: