To find the gravitational field intensity at point P, located at a vertex of an equilateral triangle with mass m at each vertex, we will analyze the contributions to the gravitational field from the other two masses.

1. Gravitational Field Concept
- The gravitational field intensity (E) at a point due to a mass is given by:
\[ E = \frac{G \cdot m}{r^2} \]
where G is the gravitational constant, m is the mass, and r is the distance from the mass to the point.

2. Setting Up the Triangle
- Consider an equilateral triangle with vertices A, B, and C, each with mass m and side length a.
- Let point P be at vertex A. The distances from A to B and A to C are both equal to a.

3. Contributions to Gravitational Field
- **From Mass at B**:
- The gravitational field at P due to mass at B:
\[ E_B = \frac{G \cdot m}{a^2} \]
- This field points towards B.
- **From Mass at C**:
- The gravitational field at P due to mass at C:
\[ E_C = \frac{G \cdot m}{a^2} \]
- This field points towards C.

4. Resultant Gravitational Field
- **Direction of Fields**:
- The fields \( E_B \) and \( E_C \) form an angle of 60° with each other.
- **Calculating the Resultant**:
- Using the cosine law, the resultant E at P can be found:
\[ E_{resultant} = E_B + E_C \cdot \cos(60^\circ) \]
- This leads to:
\[ E_{resultant} = E_B + \frac{E_C}{2} = \frac{G \cdot m}{a^2} + \frac{1}{2}\left(\frac{G \cdot m}{a^2}\right) \]
\[ E_{resultant} = \frac{3G \cdot m}{2a^2} \]

5. Final Expression
- The total gravitational field intensity at point P is:
\[ E_{P} = \frac{3G \cdot m}{2a^2} \]
- This intensity acts directly away from the center of the triangle towards point P.