pls help with a vector problem in physics?

Question

can three vectors of equal magnitude be combined to give a zero resultant? How about three vectors of unequal magnitudes? kindly explain

tnx again! :)

Answer 1

Yes, three vectors of equal magnitude can be combined in such a way that the resultant will be a zero vector. The three vectors should be 120 degrees from each other.

It is possible with three unequal vectors too but we need to first find the resultant of two and then choose a vector equal and opposite to it.

Answer 2

Take any two vectors and arrange them such that the tail end of one vector is at the head of another vector (without altering the magnitude and direction).

In short arrange the vectors in order.

Now if we can the arrange three vectors in order as the sides of a triangle,
then the resultant of these vectors is zero.

If the vectors are equal in magnitude, and if we can form an equilateral triangle, the three vectors will be in equilibrium; other wise they cannot.

Therefore, it is not enough that the three vectors are equal in magnitude; they must form a triangle to be in equilibrium.

If the magnitudes were different and still if we can form any triangle, then they will be in equilibrium.

Answer 3

Can three vectors of equal magnitude be combined to give a zero resultant?

Yes.

How about three vectors of unequal magnitudes?

Not always. Yes, if sum of any two magnitudes is higher than the third one.

Explanation is here:

http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Vectors/VectorAdditionSteps.html

http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html

http://www.ies.co.jp/math/java/vector/vsum/vsum.html

Answer 4

The value of a vector is its length. the ensuing vector is the sum of the different 2. Geometricaly, it is the third area of a triangle. If 2 vectors are at properly suited angles, the resultiant is the hypotinuse of a properly suited triangle. The lengths of the facets are the cost of the vectors. The Pythagorean theoum says that the if R is the scale (value) of the ensuing then R^2 = 17^2 + 7^2

Answer 5

Yes if three of vectors have angle of 120 degrees between each other they will cancel each other, resultant will be 0. Imagine this as rotor which has 3 arms nad angle 120 degrees between each.