Statement 1 : If `|veca | = 3, |vecb| = 4 and |veca + vecb| = 5`, then `|veca - vecb|=5`.
Statement 2 : The length of the diagonals of a rectangle is the same.

Options

A. Both the statements are true, and Statement 2 is the correct explanation for Statement 1.
B. Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.
C. Statement 1 is true and Statement 2 is false.
D. Statement 1 is false and Statement 2 is true.

Explanation

To solve the problem, we need to analyze both statements and verify their validity step by step.

### Step 1: Analyze Statement 1
We are given:
- |veca| = 3
- |vecb| = 4
- |veca + vecb| = 5

We need to determine if |veca - vecb| = 5.

### Step 2: Use the Law of Cosines
According to the law of cosines, for any two vectors veca and vecb, we have:

\[ |veca + vecb|^2 = |veca|^2 + |vecb|^2 + 2 |veca| |vecb| \cos(\theta) \]

Where \(\theta\) is the angle between veca and vecb.

Substituting the known values:

\[ 5^2 = 3^2 + 4^2 + 2 \cdot 3 \cdot 4 \cdot \cos(\theta) \]

Calculating the squares:

\[ 25 = 9 + 16 + 24 \cos(\theta) \]

This simplifies to:

\[ 25 = 25 + 24 \cos(\theta) \]

Subtracting 25 from both sides gives:

\[ 0 = 24 \cos(\theta) \]

This implies:

\[ \cos(\theta) = 0 \]

### Step 3: Determine the Angle
Since \(\cos(\theta) = 0\), it means that \(\theta = 90^\circ\). Therefore, veca and vecb are perpendicular to each other.

### Step 4: Calculate |veca - vecb|
Now we can calculate |veca - vecb| using the same law of cosines:

\[ |veca - vecb|^2 = |veca|^2 + |vecb|^2 - 2 |veca| |vecb| \cos(\theta) \]

Substituting the values:

\[ |veca - vecb|^2 = 3^2 + 4^2 - 2 \cdot 3 \cdot 4 \cdot \cos(90^\circ) \]

Since \(\cos(90^\circ) = 0\):

\[ |veca - vecb|^2 = 9 + 16 - 0 \]

This simplifies to:

\[ |veca - vecb|^2 = 25 \]

Taking the square root:

\[ |veca - vecb| = 5 \]

### Conclusion for Statement 1
Thus, Statement 1 is true: |veca - vecb| = 5.

### Step 5: Analyze Statement 2
Statement 2 states that "The length of the diagonals of a rectangle is the same." This is a known property of rectangles, and it is true.

### Final Conclusion
Both statements are true, and Statement 2 is a correct explanation for Statement 1.