Question

URGENT

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

Answer 1

Compute the components of the second vector in Cartesian coordinates. You're given the magnitude
`r=7` and direction
`\theta=\frac{2\pi}3`. In Cartesian, this vector corresponds to
`\langle x,y\rangle` where

`x=r\cos\theta=7\cos\frac{2\pi}3=-\frac72`

`y=r\sin\theta=7\sin\frac{2\pi}3=\frac{7\sqrt3}2`

Then the sum of this vector with
`\langle3,4\rangle` is

`\left\langle-\frac72,\frac{7\sqrt3}2\right\rangle+\langle3,4\rangle=\left\langle-\frac12,4+\drac{7\sqrt3}2\right\rangle`