Question

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

The sum of two vectors is (- 0.5, 10.1)

Explanation:

To add two vectors, add the corresponding components.

Let u =⟨u1,u2⟩ and v =⟨v1,v2⟩ be two vectors.

Then, the sum of u and v is the vector

u +v =⟨u1+v1, u2+v2⟩

(b)

Two vectors = ( 3, 4 )

angle 2π/3 = 120°

In x axis, the vector is = 7 cos 120°

                                    $= 7 X -\frac{1}{2} \\\\=- \frac{7}{2}$

In y axis, the vector is = 7 sin 120°

                                   = 7 X 0.866

                                   = 6.062

The second vectors are ( -3.5, 6.062)

Sum of two vectors = [( 3 + (-3.5) ), (4 + 6.062)]

                               = (- 0.5, 10.1)