Clock vectors Consider the 12 vectors that have their tails at the center of a (

Question

Clock vectors Consider the 12 vectors that have their tails at the center of a (circular) clock and their heads at the numbers on the edge of the clock. What is the sum of these 12 vectors? If the 12:00 vector is removed, what is the sum of the remaining 11 vectors? By removing one or more of these 12 clock vectors, explain how to make the sum of the remaining vectors as large as possible in magnitude. Consider the 11 vectors that originate at the number 12 at the top of the clock and point to the other 11 numbers. What is the sum of the vectors?

Explanation / Answer

a.For part (a), consider the center of the clock to be the origin. Each vector has an equal magnitude, but opposite in direction vector (12 is opposite 6, 1 is opposite 7, etc.). Adding two such opposing vectors equals zero.

[10]+[10]=[00]

So all 12 vector, 6 pairs, add to zero

C)if you remove 2 o'clock vector then you are simply left with its opposite vector which no longer is cancelled out.

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