# Determining magnitude and direction of vectors

• savva
In summary, to determine the magnitude and direction of F1 for a vertically upward resultant force of 800N, you can use the equation F1=FR-F2-F3 and solve for F1x and F1y using horizontal and vertical components. Then, use F1x and F1y to solve for F1 and θ. In this case, F1 is 274.7N and θ is 29.1 degrees.
savva

## Homework Statement

Determine the magnitude and direction θ of F1 so that the resultant force is directed vertically upward and has a magnitude of 800N.

F1=FR-F2-F3

## The Attempt at a Solution

I have attached the question with diagram and my attempt at solving the question. I know that by using the equation above, F1=FR-F2-F3, however I am slightly confused as to obtaining the values for these vectors and how to approach doing that.

#### Attachments

• Chp 2 - Q2.21 Problem.jpg
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• Chp 2 - Q2.21 Problem WORKING.jpg
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Solve for F1x using the horizontal components, solve for F1y using vertical components, then take F1x and F1y to solve for F1 and θ

Thanks for your help Joffran, I managed to solve the problem with your help, I will add the working I used to solve it tomorrow

$\Sigma$Fx=0 ----> 400cos30+F1x-(4/5)(600)=0 ----> F1x=133.6N
$\Sigma$Fy=800 ----> 400sin30+F1y+(3/5)(600)=800 ----> F1y=240N

F1= (F1x^2+F2y^2)^.5 = (133.6^2+240^2)^.5=274.7N

tanθ=F1x/F1y=133.6/240

θ=tan^-1(133.6/240)=29.1

## What is a vector?

A vector is a mathematical object that has both magnitude (size) and direction. It is represented graphically by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

## How do you determine the magnitude of a vector?

The magnitude of a vector can be determined using the Pythagorean theorem, which states that the square of the hypotenuse (longest side) of a right triangle is equal to the sum of the squares of the other two sides. In other words, the magnitude is the square root of the sum of the squares of the vector's components.

## How do you determine the direction of a vector?

The direction of a vector can be determined using trigonometric functions such as sine, cosine, and tangent. These functions can be used to find the angle between the vector and the positive x-axis, which represents the direction of the vector.

## 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 and mass, while examples of vectors include velocity and force.

## What are some real-world examples of vectors?

Vectors can be found in many real-world scenarios, such as a car traveling at a certain speed and direction, a force acting on an object, or the displacement of an object from one point to another. They are also commonly used in physics, engineering, and navigation.

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