Minimum numbar of vectors of unequal magnitudes which can give zore resultant are

Options

A. two
B. three
C. four
D. more than four

Answer

To solve the problem of finding the minimum number of vectors of unequal magnitudes that can give a zero resultant, we can follow these steps:

### Step 1: Understand the Condition for Zero Resultant
A vector sum results in zero when the vectors can be arranged in such a way that they form a closed polygon. This means that the vectors must be equal in magnitude and opposite in direction, or they must balance each other out in some way.

**Hint:** Think about how vectors can be arranged geometrically to cancel each other out.

### Step 2: Analyze One Vector
If we consider just one vector, it cannot have a zero resultant by itself unless it is a null vector (which has no magnitude). Therefore, one vector is not sufficient.

**Hint:** Consider what happens when you have only one vector and how it behaves.

### Step 3: Analyze Two Vectors
For two vectors to have a zero resultant, they must be equal in magnitude and opposite in direction. However, the question specifies that the vectors must be of unequal magnitudes. Thus, two vectors cannot satisfy the condition.

**Hint:** Reflect on the requirement for two vectors to cancel each other out.

### Step 4: Analyze Three Vectors
Now, let’s consider three vectors. It is possible to arrange three vectors of unequal magnitudes such that they can form a closed triangle. If the vectors are arranged in such a way that they connect head to tail, they will form a closed polygon, which means their vector sum will be zero.

**Hint:** Visualize how three vectors can connect to form a triangle.

### Step 5: Conclusion
Since one vector cannot give a zero resultant, and two vectors of unequal magnitudes cannot cancel each other out, the minimum number of vectors of unequal magnitudes that can give a zero resultant is three.

**Final Answer:** The minimum number of vectors of unequal magnitudes that can give a zero resultant is **3**.