# What are (a) the magnitude and (b) the angle

In summary, the problem involves finding the magnitude and angle of vector B in the equation A-> + B-> = C->, where vector A-> has a magnitude of 13.8 m and is angled 44.0° counterclockwise from the +x direction, and vector C-> has a magnitude of 16.8 m and is angled 18.8° counterclockwise from the -x direction. The solution involves using trigonometric functions to calculate the x and y components of vectors A and C, and then finding the difference vector B by subtracting the components of C from A. The magnitude of B is found by taking the square root of the sum of the squares of its x and y components

1. Homework Statement [/b]

In the sum A-> + B-> = C->, A-> vector has a magnitude of 13.8 m and is angled 44.0° counterclockwise from the +x direction, and vector C-> has a magnitude of 16.8 m and is angled 18.8° counterclockwise from the -x direction. What are (a) the magnitude and (b) the angle (relative to +x) of B->? State your angle as a positive number.

2. Homework Equations [/b]

3. The Attempt at a Solution

I don't know if its right or not. :(

sin(44)13.8 = 9.58628 for A
sin(18.8)16.8 = 5.41406368 for C
cos(44)13.8=9.926889245 for A
cos(18.8)16.8=15.90370757 for C
that's the two components of A and C. since you're trying to find B
it's C - A = B.
in the x direction: 5.41406368 - 9.58628 = -4.172
in the y direction: 15.90370757 - 9.926889245 = 5.976

The magnitude is simply sqrt (x component^2 + y component^2) = 7.288

the angle relative to +x is tan^-1(x component/y component) = tan^-1(-4.172/5.976) = -34.9 degrees.

1. Homework Statement [/b]

In the sum A-> + B-> = C->, A-> vector has a magnitude of 13.8 m and is angled 44.0° counterclockwise from the +x direction, and vector C-> has a magnitude of 16.8 m and is angled 18.8° counterclockwise from the -x direction. What are (a) the magnitude and (b) the angle (relative to +x) of B->? State your angle as a positive number.

2. Homework Equations [/b]

3. The Attempt at a Solution

I don't know if its right or not. :(

sin(44)13.8 = 9.58628 for A
sin(18.8)16.8 = 5.41406368 for C
cos(44)13.8=9.926889245 for A
cos(18.8)16.8=15.90370757 for C
that's the two components of A and C. since you're trying to find B
it's C - A = B.
in the x direction: 5.41406368 - 9.58628 = -4.172
in the y direction: 15.90370757 - 9.926889245 = 5.976

The magnitude is simply sqrt (x component^2 + y component^2) = 7.288

the angle relative to +x is tan^-1(x component/y component) = tan^-1(-4.172/5.976) = -34.9 degrees.

You are using the right methods, but I think you may have a sign wrong in one of the calculations (I could be wrong, though).

Look at where the vector C is pointing. You are given its angle of rotation from the negative x axis, not the positive one. So the x component of the C vector will be negative.

It would help clarity if you could show your answers for the two vectors A and C like this:

A = (Ax, Ay)
C = (Cx, Cy)

where you put in your numbers (with correct signs) into the parenthesis. That will help you to keep your signs right when you calculate the difference vector B. It will also help you if you sketch the vectors on paper to check that the signs and magnitudes are working out correctly.

um i don't get what your saying

## What are the magnitude and angle?

The magnitude and angle refer to the size and direction of a vector in a mathematical or physical system. The magnitude is the length or size of the vector, while the angle is the direction or orientation of the vector.

## How are magnitude and angle measured?

Magnitude is typically measured in units such as meters, kilograms, or newtons, depending on the context. Angle is measured in degrees or radians, which are units of angular measurement.

## What is the difference between magnitude and angle?

The main difference between magnitude and angle is that magnitude indicates the size or strength of a vector, while angle indicates the direction or orientation of the vector. They are both important components of a vector and are necessary for fully describing its properties.

## Can magnitude and angle be negative?

Yes, both magnitude and angle can be negative. Negative magnitude indicates a vector of opposite direction but the same size, while negative angle indicates a vector in the opposite direction from the positive angle.

## How are magnitude and angle used in physics?

In physics, magnitude and angle are important for describing the motion and forces of objects. For example, velocity and acceleration are vectors with both magnitude and angle components. In addition, forces such as weight and tension have both magnitude and angle components that determine their effects on objects.