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

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SUMMARY

The discussion focuses on finding the component form of vectors, specifically vector c = 3i + 4j and the vector from point P(0,0) to point Q(5,-2). Participants clarify that the component form of a vector is expressed as its horizontal and vertical components, represented by the coefficients of i and j. The confusion arises from the distinction between 'work' and 'component form,' with participants confirming that work is not the same as component form. The correct component form for vector v from P to Q is (5 - 0)i + (-2 - 0)j, resulting in the components 5 and -2.

PREREQUISITES
  • Understanding of vector notation (i.e., i and j components)
  • Basic knowledge of coordinate geometry
  • Familiarity with vector operations (addition and subtraction)
  • Concept of vector components and their significance
NEXT STEPS
  • Study vector addition and subtraction techniques
  • Learn about vector magnitude and direction
  • Explore applications of vectors in physics, particularly in mechanics
  • Investigate the relationship between work and energy in vector contexts
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Students studying physics or mathematics, educators teaching vector concepts, and anyone interested in understanding the component forms of vectors in coordinate systems.

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.
 

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