# 4 vectors of the same magnitude are added; 1 pointing east, 1 west, 1 south, & 1 north. resultant magnitude?

The magnitude of the resultant vector is _____.

a)0

b)1

c)2

d)3

thnx :) im stuck

### 5 Answers

- Anonymous9 years agoBest Answer
Vectors is all about direction and your visualisation.......asnwer is (a) 0 becuz going east adn then going west gets you nowhere and same for going north adn south........if vectors were not of equal magnitude asner would be different but since they are equal net asnwer is zero

- Anonymous9 years ago
a) 0

You can think of it like going a certain distance east, the same distance west, the same distance north, and the same distance south. You would end up at the same spot you started. You can also think of it as 4 equal forces pulling each other. The east and west forces are the same, so they cancel out, and the north and south forces are the same, so they cancel out as well. You are left with 0 magnitude with no direction.

If you want to prove it mathematically, let's say each of the vectors are unit vectors (magnitude = 1 ). On a coordinate grid, the North vector is (0,1) East: (1,0) South: (0,-1) and West: (-1,0). Adding all the vectors would be ( 0+1+0-1 , 1+0-1+0 ) = (0,0)

A (0,0) vector has 0 magnitude.

- Anonymous9 years ago
Well, the answer is (a). Remember when doing vector addition you just draw the vectors head to tail, and then the resulting vector is just the one drawn from the tail of the first vector to the head of the last one. Remember you can add the vectors in any order you like. So for your example, start from the origin and draw a vector pointing north (up). Then from the head of this vector draw one that points east (right). Then from the head of this one, draw another that points south (down). Finally from the head of this one draw one that points west (left). Notice that since all these vectors have the same magnitude (same length) then what you have juts done is drawn a square, and so the head of your last vector is sitting right on top of the tail of your first vector. Since there is zero distance between these the tail of the first vector and the head of the last vector, then the magnitude of the resultant vector is zero. Technically, though a vector with zero magnitude is not a vector, but even your teacher probably doesn't know that...

- 9 years ago
The answer would be zero. Think about it this way:

If you walk one mile north, and the one mile south, you are in the same position as where you started. The same goes for east and west.

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- Anonymous9 years ago
zero, cancelling out and equal magnitude contribute to this.

Source(s): studying physics at university