Assertion : The sum of squares of cosines of angles made by a vector with X, Y and Z axes is equal to unity.
Reason : A vector making `45^(@)` with X-axis must have equal components along X and Y-axes.

Options

A. If both Assertion & Reason are Tune & the Reason is a correct explanation of the Assertion. `
B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertion.
C. If Assertion is True but the Reason is False.
D. If both Assertion & Reason are false.

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states that the sum of the squares of the cosines of the angles made by a vector with the X, Y, and Z axes is equal to unity.

Let’s denote:
- The angle made by the vector with the X-axis as \( \alpha \)
- The angle made by the vector with the Y-axis as \( \beta \)
- The angle made by the vector with the Z-axis as \( \gamma \)

According to the property of vectors in three-dimensional space, we have:
\[ \cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1 \]
This is a fundamental property of vectors and is derived from the Pythagorean theorem in three dimensions. Therefore, the assertion is **true**.

### Step 2: Analyze the Reason
The reason states that a vector making an angle of \( 45^\circ \) with the X-axis must have equal components along the X and Y axes.

For a vector \( \mathbf{P} \) making an angle of \( 45^\circ \) with the X-axis, we can find its components:
- The component along the X-axis is given by \( P \cos 45^\circ \)
- The component along the Y-axis is given by \( P \sin 45^\circ \)

Since \( \cos 45^\circ = \sin 45^\circ = \frac{1}{\sqrt{2}} \), we have:
\[ \text{Component along X-axis} = P \cos 45^\circ = P \cdot \frac{1}{\sqrt{2}} \]
\[ \text{Component along Y-axis} = P \sin 45^\circ = P \cdot \frac{1}{\sqrt{2}} \]
Thus, the components along the X and Y axes are equal when the angle is \( 45^\circ \). Therefore, the reason is also **true**.

### Step 3: Determine the Relationship Between Assertion and Reason
While both the assertion and the reason are true, the reason does not provide a correct explanation for the assertion. The assertion is a general property of vectors in three-dimensional space, while the reason is a specific case about a vector at \( 45^\circ \) with the X-axis.

### Conclusion
Both the assertion and the reason are true, but the reason is not a correct explanation for the assertion. Therefore, the correct option is:
**Both assertion and reason are true, but reason is not a correct explanation for assertion.**