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

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The discussion centers on finding the component form of vectors, specifically for vector c = 3i + 4j and points P(0,0) and Q(5,-2). A participant mistakenly calculated the work of the vectors, arriving at a value of 7, and questioned whether work is the same as component form. It was clarified that work is not relevant to the component form, which focuses on the horizontal and vertical components of the vector. The correct component form for the vector from P to Q is derived as (5 - 0)i + (-2 - 0)j, resulting in the components 5 and -2. Understanding the distinction between work and component form is crucial for solving the problem correctly.
tennistudof09
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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?
 
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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.
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...

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