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 >

you forgot the options, but i found them anyways, the correct answer is "john wilson believes that words and actions based on the intellect are superior to those based on emotions".

john wilson is depicted as an extremely intelligent man. the point of the excerpt is to make a sort of distinction between emotional and rational intelligence. he happens to have both attributes, but he clearly favors his intellectual gifts. at the same time, because of his religious background, he's a little bit conflicted with this and it makes him ashamed.

hope this !

i believe the answer is c.