If a line makes angles `alpha, beta` and `gamma` with the co-ordinate axes, find `cosbeta`, if `cos alpha=14/15` and `cos gamma=-1/3`.

Explanation

To solve the problem, we need to find \( \cos \beta \) given \( \cos \alpha = \frac{14}{15} \) and \( \cos \gamma = -\frac{1}{3} \). We will use the relationship between the direction cosines of a line and the angles it makes with the coordinate axes.

### Step-by-step Solution:

1. **Understanding the Relationship**:
The direction cosines \( l, m, n \) of a line making angles \( \alpha, \beta, \gamma \) with the coordinate axes are defined as:
\[
l = \cos \alpha, \quad m = \cos \beta, \quad n = \cos \gamma
...