Answer:
The sum of the two vectors is the vector <-0.5 , 4+3.5[tex]\sqrt{3}[/tex] >
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 [tex]\frac{2\pi }{3}[/tex]
- That means its magnitude is 7 and its direction is [tex]\frac{2\pi }{3}[/tex]
∴ x = 7 cos( [tex]\frac{2\pi }{3}[/tex] )
∴ y = 7 sin( [tex]\frac{2\pi }{3}[/tex] )
∵ cos( [tex]\frac{2\pi }{3}[/tex] ) = [tex]-\frac{1}{2}[/tex]
∵ sin( [tex]\frac{2\pi }{3}[/tex] ) = [tex]\frac{\sqrt{3}}{2}[/tex]
- Substitute them in x and y
∴ x = (7)( [tex]-\frac{1}{2}[/tex] )
∴ x = -3.5
∴ y = (7)( [tex]\frac{\sqrt{3}}{2}[/tex] )
∴ y = 3.5[tex]\sqrt{3}[/tex]
∴ The vector is <-3.5 , 3.5[tex]\sqrt{3}[/tex]>
Now lets add the vectors by adding xs and ys components
∵ <3 , 4> + <-3.5 , 3.5[tex]\sqrt{3}[/tex] > = <3 + -3.5 , 4 + 3.5[tex]\sqrt{3}[/tex] >
∴ <3 , 4> + <-3.5 , 3.5[tex]\sqrt{3}[/tex]> = <-0.5 , 4+3.5[tex]\sqrt{3}[/tex] >
∴ The sum of the two vectors is the vector <-0.5 , 4+3.5[tex]\sqrt{3}[/tex] >
