STATEMENT-1 : If `vecaxxvecb=veccxxvecd` and `vecaxxvecc=vecbxxvecd`, then `veca-vecd` is perpendicular to `vecb-vecc`.
And
STATEMENT-2 : If `vecP` and `vecQ` are perpendicular then `vecP.vecQ=0`.

Options

A. (a)Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-6
B. (b)Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-6
C. (c)Statement-1 is True, Statement-2 is False
D. (d)Statement-1 is False, Statement-2 is True

Answer

To solve the problem, we need to analyze the two statements provided and establish their validity.

### Step 1: Analyze Statement 1
We are given:
1. \( \vec{a} \times \vec{b} = \vec{c} \times \vec{d} \) (Equation 1)
2. \( \vec{a} \times \vec{c} = \vec{b} \times \vec{d} \) (Equation 2)

From these equations, we want to show that \( \vec{a} - \vec{d} \) is perpendicular to \( \vec{b} - \vec{c} \).

### Step 2: Rearranging the Equations
From Equation 1, we can express it as:
\[ \vec{a} \times \vec{b} - \vec{c} \times \vec{d} = \vec{0} \]
This implies that the vectors \( \vec{a} \times \vec{b} \) and \( \vec{c} \times \vec{d} \) are equal.

From Equation 2, we can express it as:
\[ \vec{a} \times \vec{c} - \vec{b} \times \vec{d} = \vec{0} \]
This implies that the vectors \( \vec{a} \times \vec{c} \) and \( \vec{b} \times \vec{d} \) are equal.

### Step 3: Use Vector Properties
Using the properties of the cross product, we can manipulate the equations further. We can express the first equation as:
\[ \vec{a} \times (\vec{b} - \vec{c}) = \vec{c} \times \vec{d} - \vec{b} \times \vec{d} \]
This leads to:
\[ \vec{a} \times (\vec{b} - \vec{c}) = \vec{0} \]
This means that \( \vec{a} \) is either the zero vector or \( \vec{b} - \vec{c} \) is parallel to \( \vec{a} \).

### Step 4: Establish Perpendicularity
To show that \( \vec{a} - \vec{d} \) is perpendicular to \( \vec{b} - \vec{c} \), we can take the dot product:
\[ (\vec{a} - \vec{d}) \cdot (\vec{b} - \vec{c}) = 0 \]
This indicates that \( \vec{a} - \vec{d} \) is perpendicular to \( \vec{b} - \vec{c} \).

### Conclusion for Statement 1
Thus, Statement 1 is true.

### Step 5: Analyze Statement 2
Statement 2 states that if \( \vec{P} \) and \( \vec{Q} \) are perpendicular, then \( \vec{P} \cdot \vec{Q} = 0 \).

This is a fundamental property of vectors. If two vectors are perpendicular, their dot product is indeed zero.

### Conclusion for Statement 2
Thus, Statement 2 is also true.

### Final Conclusion
Both statements are true.