**Given Data:**
- Mass of the particle, m = 2 kg
- Initial velocity along the x-axis, u = 10 m/s
- Final velocity along the y-axis, v = 10 m/s
- Time taken, t = 5 s

**Determination of Change in Linear Momentum:**

The change in linear momentum of an object is given by the formula:

Δp = m * (v - u)

where Δp is the change in linear momentum, m is the mass of the object, v is the final velocity, and u is the initial velocity.

**Determination of Change in Linear Momentum in the i-component:**

As the particle changes its velocity from the x-axis to the y-axis, the change in linear momentum in the i-component can be determined by considering the change in velocity along the x-axis.

Δp_i = m * (v_i - u_i)

where Δp_i is the change in linear momentum in the i-component, m is the mass of the particle, v_i is the final velocity along the x-axis, and u_i is the initial velocity along the x-axis.

Since the particle's velocity changes from 10 m/s along the x-axis to 0 m/s along the x-axis, the change in linear momentum in the i-component can be calculated as:

Δp_i = 2 kg * (0 m/s - 10 m/s)

Δp_i = -20 kg·m/s

Therefore, the magnitude of the change in linear momentum in the i-component is 20 kg·m/s, and the direction is negative along the x-axis.

**Determination of Change in Linear Momentum in the j-component:**

As the particle changes its velocity from the x-axis to the y-axis, the change in linear momentum in the j-component can be determined by considering the change in velocity along the y-axis.

Δp_j = m * (v_j - u_j)

where Δp_j is the change in linear momentum in the j-component, m is the mass of the particle, v_j is the final velocity along the y-axis, and u_j is the initial velocity along the y-axis.

Since the particle's velocity changes from 0 m/s along the y-axis to 10 m/s along the y-axis, the change in linear momentum in the j-component can be calculated as:

Δp_j = 2 kg * (10 m/s - 0 m/s)

Δp_j = 20 kg·m/s

Therefore, the magnitude of the change in linear momentum in the j-component is 20 kg·m/s, and the direction is positive along the y-axis.

**Summary:**

The magnitude and direction of the change in linear momentum in component (i,j) are as follows:

- Change in Linear Momentum in the i-component: 20 kg·m/s, negative along the x-axis
- Change in Linear Momentum in the j-component: 20 kg·m/s, positive along the y-axis