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The locus of point of intersection of the perpendicular lines:

To find the locus of the point of intersection of the perpendicular lines, we need to find the equations of the lines and their point of intersection. Let's start by finding the equations of the given lines.

Finding the equation of the first line:
The given line is represented by the equation (x y-2) λ(x 3y-5) = 0. Expanding this equation, we get:
x(x + 3y - 5λ) + y(λ - 2) = 0

The equation of the first line is of the form Ax + By + C = 0, where A = (1 + 3λ), B = (λ - 2), and C = 0.

Finding the equation of the second line:
The second line is represented by the equation (2x 3y-11) λ'(2x 2y- 13) = 0. Expanding this equation, we get:
2x(2x + 2y - 13λ') + 3y(λ' - 11) = 0

The equation of the second line is of the form Dx + Ey + F = 0, where D = (4 + 4λ'), E = (3λ' - 33), and F = 0.

Finding the point of intersection:
To find the point of intersection, we need to solve the equations of the two lines simultaneously. By equating the coefficients of x, y, and the constant term, we can determine the values of λ and λ'.

After solving the equations, we obtain the values of λ and λ'. Substituting these values back into the equations of the lines, we can find the coordinates of the point of intersection.

Finding the locus:
The locus of the point of intersection is the set of all points that satisfy the given conditions. In this case, the locus will be a curve or a line.

To determine the exact form of the locus, we need to analyze the values of λ and λ' and their relationship. Depending on the values, the locus can be a line, a curve, or a combination of both.

Summary:
1. Find the equations of the given lines.
2. Determine the point of intersection by solving the equations simultaneously.
3. Substitute the values of λ and λ' back into the equations to find the coordinates of the point of intersection.
4. Analyze the values of λ and λ' to determine the form of the locus.
5. The locus can be a line, a curve, or a combination of both, depending on the values of λ and λ'.