Two vectors of magnitudes 10 and 15 units can never have a resultant equal to

Options

A. 15 units
B. 3 units
C. 10 units
D. 20 units

Explanation

To solve the problem of determining which resultant cannot be achieved by two vectors of magnitudes 10 and 15 units, we can follow these steps:

### Step 1: Understand the Range of Resultant Vectors
The resultant \( R \) of two vectors can vary based on their magnitudes and the angle between them. The range of possible values for the resultant can be defined by:
- The minimum resultant \( R_{min} = |A - B| \)
- The maximum resultant \( R_{max} = A + B \)

Where \( A \) and \( B \) are the magnitudes of the two vectors.

### Step 2: Calculate the Minimum and Maximum Resultant
Given the magnitudes:
- \( A = 10 \) units
- \( B = 15 \) units

We can calculate:
- Minimum resultant:
\[ R_{min} = |10 - 15| = | -5 | = 5 \text{ units} \]
- Maximum resultant:
\[ R_{max} = 10 + 15 = 25 \text{ units} \]

### Step 3: Determine the Range of Possible Resultants
The possible values for the resultant \( R \) must lie between the minimum and maximum values:
\[ 5 \leq R \leq 25 \]

### Step 4: Identify Values Outside the Range
Any resultant value that is less than 5 or greater than 25 cannot be achieved by these two vectors.

### Step 5: Check Given Options
We need to check which of the given options falls outside the range of 5 to 25.

Assuming the options are:
1. 3 units
2. 15 units
3. 10 units
4. 20 units

From these:
- 3 units is less than 5 (not possible)
- 15 units is within the range (possible)
- 10 units is within the range (possible)
- 20 units is within the range (possible)

### Conclusion
The only value that cannot be achieved as a resultant of the two vectors is **3 units**.