A vector having magnitude 30 unit makes equal angles with each of X,Y, and Z -axes The components of vector along each of X,Y,and Z -axes are

Options

A. `10sqrt(3) ` unit
B. `20sqrt(3)` unit
C. `15sqrt(3)` unit
D. 10 unit

Explanation

To find the components of a vector that has a magnitude of 30 units and makes equal angles with each of the X, Y, and Z axes, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have a vector \( \vec{A} \) with a magnitude of 30 units. It makes equal angles with the X, Y, and Z axes. We need to find the components of this vector along each axis.

2. **Setting Up the Components**:
Let the components of the vector along the X, Y, and Z axes be \( A_x \), \( A_y \), and \( A_z \) respectively. Since the vector makes equal angles with all axes, we can denote:
\[ A_x = A_y = A_z = A \]

3. **Using the Magnitude Formula**:
The magnitude of the vector \( \vec{A} \) can be expressed in terms of its components:
\[ |\vec{A}| = \sqrt{A_x^2 + A_y^2 + A_z^2} \]
Substituting \( A_x = A_y = A_z = A \):
\[ |\vec{A}| = \sqrt{A^2 + A^2 + A^2} = \sqrt{3A^2} = A\sqrt{3} \]

4. **Setting the Magnitude Equal to 30**:
We know that the magnitude of the vector is given as 30 units:
\[ A\sqrt{3} = 30 \]

5. **Solving for A**:
To find \( A \), we can rearrange the equation:
\[ A = \frac{30}{\sqrt{3}} \]
To simplify this, we can rationalize the denominator:
\[ A = \frac{30 \sqrt{3}}{3} = 10\sqrt{3} \]

6. **Finding the Components**:
Since \( A_x = A_y = A_z = A \), we have:
\[ A_x = A_y = A_z = 10\sqrt{3} \]

### Final Answer:
The components of the vector along the X, Y, and Z axes are:
\[ A_x = A_y = A_z = 10\sqrt{3} \]