# Finding Component Form of Vectors: c, P, and Q

• tennistudof09
In summary, the problem is asking to find and state the component form of the given vectors. The component form of a vector is represented as v = ai + bj, where a is the horizontal component and b is the vertical component. In this problem, the vectors are c = 3i + 4j, P(0,0), and Q(5,-2). The component form of these vectors would be (5-0)i + (-2-0)j, which simplifies to 5i - 2j.The student mistakenly found the work of the problem, which is not the same as the component form. The work is found by multiplying the magnitude of the vector by the distance it is moved. In
tennistudof09
the problem says:

find and state the component form of the following vectors.
c= 3i + 4j P(0,0),Q(5,-2)

for some reason, i think i ended up doing unneccessary work. I found the Work of the problem instead, which is 7. Is work the same thing as component form? If not, what am I supposed to be looking for?

tennistudof09 said:
the problem says:

find and state the component form of the following vectors.
c= 3i + 4j P(0,0),Q(5,-2)

for some reason, i think i ended up doing unneccessary work. I found the Work of the problem instead, which is 7. Is work the same thing as component form? If not, what am I supposed to be looking for?
Work? How does work enter into a problem that asks for the compenents?

If v = ai + bj, the horizontal component is a and the vertical component is b.

If v is the vector from P(a, b) to Q(c, d), v = (c - a)i + (d - b)j and its components are c -a and d - b.

Hello,

Thank you for sharing the problem and your solution. It seems like you may have misunderstood the task at hand. The problem is asking you to find the component form of the vectors c, P, and Q. This means that you need to express each vector in terms of its x and y components.

Let's break down the problem and see how to find the component form of each vector:

1. Vector c = 3i + 4j
The notation i and j represent the unit vectors in the x and y directions, respectively. Therefore, the x component of vector c is 3 and the y component is 4. So the component form of vector c is (3,4).

2. Vector P(0,0)
This vector is already in component form. The x and y components are both 0.

3. Vector Q(5,-2)
Similarly, this vector is also already in component form. The x component is 5 and the y component is -2.

So, the component forms of the given vectors are:
c = (3,4)
P = (0,0)
Q = (5,-2)

In summary, work and component form are not the same thing. Work is a measure of the energy transferred by a force, while component form refers to the expression of a vector in terms of its x and y components. I hope this clarifies your confusion. Keep up the good work in your studies!

## 1. What is the component form of a vector?

The component form of a vector is a way of representing a vector in terms of its horizontal and vertical components. It is usually written in the form c = (a, b), where a is the horizontal component and b is the vertical component.

## 2. How do I find the component form of a vector?

To find the component form of a vector, you will need to know the magnitude and direction of the vector. You can then use trigonometry to calculate the horizontal and vertical components of the vector.

## 3. What are the variables c, P, and Q in the component form of a vector?

In the component form of a vector, c represents the entire vector, while P represents the horizontal component and Q represents the vertical component. So, c = (P, Q).

## 4. Can the component form of a vector be negative?

Yes, the component form of a vector can have negative values for both the horizontal and vertical components. This would indicate that the vector is pointing in the opposite direction of the positive axes.

## 5. Why is it important to know the component form of a vector?

The component form of a vector is important because it allows you to easily calculate the magnitude and direction of a vector. It also makes it easier to perform mathematical operations on vectors, such as addition, subtraction, and multiplication.

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