Assertion: If the rectangular components of a force are 24N and 7N, then the magnitude of the force is 25N.
Reason : If `|vecA|=|vecN|=1` then `|vecAxxvecN|^(2)+|vecA.vecN|^(2)=1`

Options

A. Pressure, Young's modulus, Stress
B. Emf, Potential difference, Electric Potential
C. Heat, Work done, Energy
D. Dipole moment, Electric flux, Electric field

Explanation

To solve the given question, we will analyze both the assertion and the reason step by step.

### Step 1: Analyze the Assertion
The assertion states that if the rectangular components of a force are 24 N and 7 N, then the magnitude of the force is 25 N.

**Solution:**
To find the magnitude of the force (F), we can use the Pythagorean theorem since the components are perpendicular to each other. The formula for the magnitude of a vector with components \(Ax\) and \(Ay\) is:

\[ F = \sqrt{Ax^2 + Ay^2} \]

Here, \(Ax = 24 \, \text{N}\) and \(Ay = 7 \, \text{N}\).

Substituting the values:

\[ F = \sqrt{(24)^2 + (7)^2} = \sqrt{576 + 49} = \sqrt{625} = 25 \, \text{N} \]

Thus, the assertion is true.

### Step 2: Analyze the Reason
The reason states that if \(|\vec{A}| = |\vec{N}| = 1\), then \(|\vec{A} \times \vec{N}|^2 + |\vec{A} \cdot \vec{N}|^2 = 1\).

**Solution:**
We need to verify this statement.

1. The magnitude of the cross product of two vectors can be expressed as:
\[ |\vec{A} \times \vec{N}| = |\vec{A}| |\vec{N}| \sin \theta \]
where \(\theta\) is the angle between the two vectors.

2. The magnitude of the dot product of two vectors can be expressed as:
\[ |\vec{A} \cdot \vec{N}| = |\vec{A}| |\vec{N}| \cos \theta \]

3. Since \(|\vec{A}| = 1\) and \(|\vec{N}| = 1\), we can simplify these expressions:
\[ |\vec{A} \times \vec{N}| = \sin \theta \]
\[ |\vec{A} \cdot \vec{N}| = \cos \theta \]

4. Now, substituting these into the equation given in the reason:
\[ |\vec{A} \times \vec{N}|^2 + |\vec{A} \cdot \vec{N}|^2 = \sin^2 \theta + \cos^2 \theta \]

5. We know from trigonometry that:
\[ \sin^2 \theta + \cos^2 \theta = 1 \]

Thus, the reason is also true.

### Conclusion
Both the assertion and the reason are true, but the reason does not provide a correct explanation for the assertion.