# Vectors, magitude, scalar components

• brittbc
In summary, the displacement vectors A, B, and C are given with their corresponding scalar components and magnitudes. To determine which two vectors are equal, we can compare their magnitudes. It is given that vector A and vector C have the same magnitude of 100.0 m, and to support this choice, we can calculate that both vectors are directed at an angle of 36.9 degrees above the + x axis. Therefore, vector A and vector C are the two equal vectors.
brittbc

## Homework Statement

the displacement vector A has scalr omponents of Ax= 80.0 m and Ay= 60.0 m. the displacement vector B has a scalr component Bx= 60.0 m and a magnitude of B=75.0m. The displacement vecto C has a magnitude of C= 100.0 m and is directed at an angle of 36.9 degrees above the + x axis. Two of these vectors are equal. determine which two, and support your choice with a calculation.

## The Attempt at a Solution

vector A= 100m
By= 45m
vector A= vector C

So vector A and vector C have the same magnitude. Can you show they're both 36.9 degrees above the x-axis.

The two vectors that are equal are A and C. This can be determined by calculating the magnitude of vector A using the Pythagorean theorem: A = √(Ax^2 + Ay^2) = √(80.0m^2 + 60.0m^2) = √(6400m^2 + 3600m^2) = √10000m^2 = 100m. This is the same magnitude as vector C, which is also 100m. Additionally, the angle of vector C, 36.9 degrees, is the same as the angle between the +x axis and vector A, making them equal in direction as well. Therefore, vector A and vector C are equal.

## 1. What is a vector?

A vector is a mathematical object that has both magnitude and direction. It is represented by an arrow pointing in the direction of its magnitude, and its length represents its magnitude.

## 2. How is the magnitude of a vector calculated?

The magnitude of a vector is calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In the case of a vector, the magnitude is equal to the square root of the sum of the squares of its components.

## 3. What are scalar components?

Scalar components are the individual parts of a vector that are parallel to the x and y axes. They are used to represent the magnitude and direction of a vector in a two-dimensional space.

## 4. How are vector components calculated?

Vector components can be calculated using trigonometric functions, specifically the cosine and sine functions. The x-component is equal to the magnitude of the vector multiplied by the cosine of the angle between the vector and the x-axis, while the y-component is equal to the magnitude of the vector multiplied by the sine of the angle.

## 5. What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. Examples of scalars include temperature, mass, and time, while examples of vectors include displacement, velocity, and force.

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