Can `(1/sqrt3,1/sqrt2,1/sqrt2)` be direction cosines of a vector.

Explanation

To determine whether the values \( \left( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right) \) can be direction cosines of a vector, we need to verify if they satisfy the property of direction cosines. The property states that the sum of the squares of the direction cosines must equal 1.

### Step-by-Step Solution:

1. **Identify the Direction Cosines**:
Let \( l = \frac{1}{\sqrt{3}} \), \( m = \frac{1}{\sqrt{2}} \), and \( n = \frac{1}{\sqrt{2}} \).

2. **Apply the Property of Direction Cosines**:
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