Finding the sum vector given only the moduli and angle

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    Angle Sum Vector
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SUMMARY

The problem involves finding the modulus of the sum vector \overline{s} resulting from two vectors \overline{a} and \overline{b} with moduli 3u and 4u, respectively, and an angle of 120 degrees between them. The correct approach to solve this is by applying the cosine rule, specifically the formula \(|\overline{s}| = \sqrt{|\overline{a}|^2 + |\overline{b}|^2 + 2|\overline{a}||\overline{b}|\cos(120^\circ)}\). This leads to the modulus of the sum vector being 5u. The angle between \overline{s} and \overline{a} can be determined using the law of sines or by further trigonometric analysis.

PREREQUISITES
  • Understanding of vector addition and properties
  • Familiarity with the cosine rule in trigonometry
  • Knowledge of dot product calculations
  • Basic trigonometric functions and their applications
NEXT STEPS
  • Study the cosine rule in detail, particularly in the context of vector addition
  • Learn about the law of sines and its application in vector angle calculations
  • Practice problems involving vector moduli and angles
  • Explore vector representation in polar coordinates for better visualization
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Students studying physics or mathematics, particularly those focusing on vector analysis and trigonometry, as well as educators looking for problem-solving techniques in vector addition scenarios.

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Homework Statement


Given two 2-dimensional vectors [itex]\overline{a}[/itex] and [itex]\overline{b}[/itex] of moduli l[itex]\overline{a}[/itex]l = 3u and l[itex]\overline{b}[/itex]l = 4u, and forming an
angle  of 120 degrees between them, determine the modulus of the sum vector [itex]\overline{s}[/itex] = [itex]\overline{a}[/itex] + [itex]\overline{b}[/itex]
and the angle between [itex]\overline{s}[/itex] and [itex]\overline{a}[/itex].


Homework Equations



a.b = l[itex]\overline{a}[/itex]ll[itex]\overline{b}[/itex]lcosθ

The Attempt at a Solution



All if have calculated is the dot product of vectors a and b, coming to (6u2). I cannot seem to figure out what I can do to find the sum of these vectors only given the moduli and angle between them. Please Help :-)
 
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I think I have solved my own question. I think I have to use the cosine rule and not the vector product rule as stated above
 
K.QMUL said:
I think I have solved my own question. I think I have to use the cosine rule and not the vector product rule as stated above

What do you get for your answers?
 

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