can two vectors of diffrent magnitude be combined to give a zero resultant ?

Yes, two vectors of different magnitudes can be combined to give a zero resultant, but this occurs under specific conditions. To understand this, let's delve into the concept of vector addition and the conditions required for achieving a zero resultant.

Understanding Vector Addition

Vectors are quantities that have both magnitude and direction. When we add vectors, we consider both these aspects. The resultant vector is the vector that represents the combined effect of the individual vectors.

Conditions for Zero Resultant

For two vectors to combine and yield a zero resultant, they must be equal in magnitude but opposite in direction. This means that if one vector points in a certain direction, the other must point directly opposite to it. Mathematically, if we have two vectors, **A** and **B**, the condition for a zero resultant can be expressed as:

• If **A** = 5 units to the right, then **B** must be 5 units to the left.
• In terms of angles, if **A** is at 0 degrees, then **B** must be at 180 degrees.

Combining Vectors of Different Magnitudes

Now, if we consider two vectors of different magnitudes, say **A** = 5 units and **B** = 3 units, they cannot combine to give a zero resultant. The reason is that the vector with the larger magnitude will always dominate the smaller one, resulting in a net vector that points in the direction of the larger vector. In this case:

• **A** = 5 units to the right
• **B** = 3 units to the right
• Resultant = 5 + 3 = 8 units to the right

However, if we had two vectors that were equal in magnitude but opposite in direction, such as **A** = 5 units to the right and **B** = 5 units to the left, the resultant would indeed be zero:

• **A** = 5 units to the right
• **B** = 5 units to the left
• Resultant = 5 - 5 = 0 units

Visualizing the Concept

Imagine you are on a straight road. If you walk 5 meters forward (this is vector **A**) and then walk 5 meters backward (this is vector **B**), you end up where you started. This is a practical example of how two equal but opposite vectors can result in a zero net movement.

Conclusion

In summary, while two vectors of different magnitudes cannot combine to yield a zero resultant, two vectors of equal magnitude in opposite directions can. This principle is fundamental in physics and engineering, where understanding forces and their resultant effects is crucial.