What is the value of a.(b + c) in a Regular Hexagon?

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SUMMARY

The value of the expression a.(b + c) in a regular hexagon PRQSTU, where each side measures 2 units, can be determined by analyzing the angular relationships and vector components. The vectors a, b, and c correspond to the segments PQ, QR, and RS respectively. A clear diagram of the hexagon reveals the geometric relationships necessary to compute the dot product accurately. Understanding the angles and lengths of these vectors is crucial for solving the problem effectively.

PREREQUISITES
  • Understanding of vector notation and operations
  • Familiarity with regular hexagon properties
  • Knowledge of trigonometric relationships in geometry
  • Ability to compute dot products of vectors
NEXT STEPS
  • Study vector operations, focusing on dot products and their geometric interpretations
  • Learn about the properties of regular polygons, specifically hexagons
  • Explore trigonometric functions and their applications in vector analysis
  • Practice drawing and analyzing vector diagrams for complex shapes
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Students studying geometry and vector mathematics, educators teaching vector operations, and anyone preparing for exams involving geometric vector problems.

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Homework Statement



"PRQSTU is a regular hexagon of side 2 units. PQ,QR and RS represent vectors a, b andc respectively. Find the value of a.(b + c)

The hexagon is a regular hexagon starting at the far left (ie pointing left) with P then anti clockwise through U at the top left.

Homework Equations



None that I can think of.

The Attempt at a Solution



I really don't know where to start. I've guessed that a (PQ) = -c. But I don't know where to go from there and now I'm really confused.

Any help greatly appreciated.
 
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You must be drawing a pretty horrid picture of a hexagon to be guessing that a=(-c). If you draw a neat picture you will probably realize there is a special angular relationship between a and b+c. You could also just tough it out and compute the components of the vectors a, b and c, since you know their lengths and the angles between them.
 
Thanks for the reply.

I think I realized why I was lost - it's because I was! We haven't been taught this part of vectors yet, and I was looking at a past paper.

Haha, oops. The picture was already printed for me and I thought that a=(-c). I better stick to diagrams of squares. :)
 

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