Question

Construct c = a + b by drawing and calculating the direction and magnitude of c. The direction should be

Answer 1

the method of the coordinates we can find the vector sum of the two vectors given, therefore the answer is:

              c = 10.15

              a = 70.4º

measured counterclockwise from the positive side of the x-axis

given parameters

• vectors a and b

to find

• the vector adds

The sum of vectors must take into account finding both the magnitude of the vector that is a scalar and its direction.

One of the best methods to perform vector addition is to add their component and then find the resulting vector.

Let's use trigonometry to find the components of vectors a and b, we take the data from the diagram.

Vector a

magnitude m_a = 8.0

angle  θ= 45º   in the second quadrant

           cos 45 = x_a / m_a

           sin 45 = y_a / m_a

           x_a = m_a cos 45

           y_a = m_a sin 45

           x_a = 8.0 cos 45 = 5.657

           y_a = 8.0 sin 45 = 5.657

as we are in the second quadrant, see diagram

          x_a = - 5,657

          y_a = 5,627

     

Vactor b

magnitude m_b = 4.5

angle  θ = 60º   in the first quadrant

             cos 60 = x_b / m_b

             sin 60 = y_b / m_b

             x_b = m_b cos 60

             y_b = m_b sin 60

             x_b = 4.5 cos 60 = 2.25

             y_b = 4.5 sin 60 = 3.897

Having the components encode the components of the resulting vector

             cₓ = x_a + x_b

             c_y = y_a + y_b

             cₓ = - 5.657 + 2.25 = 3.407

             c_y = 5,657 + 3,897 = 9,554

With these values ​​we can find the modulus of the vector using the Pythagoras Theorem

             c = $\sqrt{c_x^2 + c_y^2}$

             c = $\sqrt{3.407^2 + 9.554^2}$

             c = 10.14

for the angle we must use the trigonometry relations

             tan  θ = $\frac{c_y}{c_x}$    

              θ = tan⁻¹ $\frac{c_y}{c_x}$

              θ = tan⁻¹ $\frac{9.554}{3.407}$

              θ = 70.4º

In conclusion with the method of coordinates we can find the resulting vector

             magnitud  c= 10.15

             angle  θ = 70.4º

measured counterclockwise from the positive side of the x axis

learn more about vector addition here:

brainly.com/question/15074838