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**What are the resultant components of the vectors?**

## Homework Statement

Determine the sum of the following three vectors. Give the resultant in terms of a. components, b. magnitude and angle with x-axis.

Vector A has a magnitude of 66 at an angle of 28 degrees northeast (quadrant 1)

Vector B has a magnitude of 40 at an angle of 56 degrees northwest (quadrant 2)

Vector C has a magnitude of 46.8 at an angle of 0 (on y-axis between Quadrant 3 and 4)

## Homework Equations

Vx = Dcos0

Vy = Dsin0

Vx = V1x+V2x+V3x

Vy = V1y+V2y+V3y

Vy/Vx = tan θ

## The Attempt at a Solution

So here is how I started

A: Vx = +(66)(cos 28) = 58.27454

Vy = +(66) (sin 28) = 30.985

B: Vx = -(40)(cos 56) = -22.3677

Vy = +(40)(sin 56) = 33.1615

C: Vx = (46.8)(cos 0) = 46.8

Vy = (46.8) (sin 0) = 0

Then I would add the three parts of Vx to get overall Vx (58.27454-22.3677+46.8) = 82.70684 & the three parts of Vy to get overall Vy (30.085+33.1615+0) = 63.2467.

This means the components would be (82.70684, 63.2467) and I would continue with pythagorean theorem to get the magnitude & use the arctan formula to get the angle. However, my answer for components is incorrect, the book says it should be (35.9,17.3). What did I do wrong? Thank you so much in advance.

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