# Position vector and magnitude problem

• xgoddess210
In summary, the problem asks for the value of the y-component of a position vector in the first quadrant with an x-component of 6.0m and a magnitude of 10m. The magnitude represents the hypotenuse in a right triangle and can be used to solve for the y-component.
xgoddess210

## Homework Statement

A position vector in the first quadrant has an x-component of 6.0m and a magnitude of 10m

What is the value of its y-component?

?

## The Attempt at a Solution

Well I originally thought I could draw a graph where x=6 and y=...then I realized i was solving for y. I don't know what the magnitude bit means. I thought it meant direction, but I don't see how that applies or would help me solve the problem. A little advice on how to solve this problem would be lovely!

Treat this as a right angle triangle

The magnitude would be the hypotenuse in this case

As a scientist, it is important to understand the concepts behind the problem before attempting to solve it. In this case, a position vector is a mathematical representation of a point in space, which consists of an x-component and a y-component. The magnitude of a vector is its length or size, and it is always a positive value.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the magnitude of the position vector is the hypotenuse, and the x- and y-components are the other two sides.

So, we can set up the equation:

10m^2 = (6.0m)^2 + y^2

Solving for y, we get:

y = √(10m^2 - (6.0m)^2)

y = √(100m^2 - 36.0m^2)

y = √64m^2

y = 8m

Therefore, the y-component of the position vector is 8m. It is important to understand the concepts of position vectors and magnitude in order to accurately solve problems like this one.

## 1. What is a position vector?

A position vector is a mathematical representation of the location of a point in space relative to a reference point. It is typically denoted by the symbol r and is expressed in terms of its x, y, and z components.

## 2. How is a position vector different from a displacement vector?

A position vector represents the location of a point in space, while a displacement vector represents the change in position of a point from its initial position to its final position. In other words, a position vector is a fixed vector that describes a point's location, while a displacement vector is a variable vector that describes the change in position of a point.

## 3. What is the magnitude of a position vector?

The magnitude of a position vector is its length or size. It is calculated using the Pythagorean theorem, which states that the magnitude of a vector r with components x, y, and z is given by the equation |r| = √(x² + y² + z²).

## 4. How can position vectors be used in physics?

Position vectors are an essential tool in physics as they help describe the position and movement of objects in space. They are used in kinematics to analyze the motion of objects, in Newton's laws of motion to calculate forces, and in vectors to represent physical quantities such as velocity and acceleration.

## 5. Can a position vector have negative components?

Yes, a position vector can have negative components. The negative sign indicates the direction of the vector component, with positive values representing a displacement in the positive direction and negative values representing a displacement in the negative direction. This is important in physics as it helps determine the direction of an object's movement in relation to a reference point.

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