If the perpendicular distance of the point `(6 5, 8)` from the `y`-axis is `5lambda` units, then `lambda` is equal to ___

Answer

To solve the problem, we need to find the value of \( \lambda \) given that the perpendicular distance of the point \( (6, 5, 8) \) from the \( y \)-axis is \( 5\lambda \) units.

### Step-by-step Solution:

1. **Identify the Coordinates**: The point given is \( (6, 5, 8) \). Here, the \( x \)-coordinate is \( 6 \), the \( y \)-coordinate is \( 5 \), and the \( z \)-coordinate is \( 8 \).

2. **Understand the Distance from the \( y \)-axis**: The perpendicular distance of any point from the \( y \)-axis is determined solely by its \( x \)-coordinate. This is because the \( y \)-axis is defined by \( x = 0 \). Therefore, the distance from the point \( (x, y, z) \) to the \( y \)-axis is simply \( |x| \).

3. **Calculate the Distance**: For the point \( (6, 5, 8) \), the distance from the \( y \)-axis is:
\[ \text{Distance} = |6| = 6 \text{ units} \]

4. **Set Up the Equation**: According to the problem, this distance is also equal to \( 5\lambda \). Therefore, we can write:
\[ 6 = 5\lambda \]

5. **Solve for \( \lambda \)**: To find \( \lambda \), we divide both sides of the equation by \( 5 \):
\[ \lambda = \frac{6}{5} \]

### Conclusion:
Thus, the value of \( \lambda \) is \( \frac{6}{5} \).

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