A

Step 1: Resolve each vector into its components.
For vector A:
Magnitude = 100 units, Angle = 45º
A_x = 100 * cos(45º) = 100 * \frac{\sqrt{2}}{2} = 50\sqrt{2}
A_y = 100 * sin(45º) = 100 * \frac{\sqrt{2}}{2} = 50\sqrt{2}

For vector B:
Magnitude = 100 units, Angle = 135º
B_x = 100 * cos(135º) = 100 * -\frac{\sqrt{2}}{2} = -50\sqrt{2}
B_y = 100 * sin(135º) = 100 * \frac{\sqrt{2}}{2} = 50\sqrt{2}

For vector C:
Magnitude = 100 units, Angle = 315º
C_x = 100 * cos(315º) = 100 * \frac{\sqrt{2}}{2} = 50\sqrt{2}
C_y = 100 * sin(315º) = 100 * -\frac{\sqrt{2}}{2} = -50\sqrt{2}

Step 2: Sum the components of the vectors:
Total X-component = A_x + B_x + C_x = 50\sqrt{2} - 50\sqrt{2} + 50\sqrt{2} = 50\sqrt{2}

Total Y-component = A_y + B_y + C_y = 50\sqrt{2} + 50\sqrt{2} - 50\sqrt{2} = 50\sqrt{2}

Step 3: In resultant vector R, we have:
R_x = 50\sqrt{2}
R_y = 50\sqrt{2}

R = \sqrt{(R_x^2 + R_y^2)} = \sqrt{((50\sqrt{2})^2 + (50\sqrt{2})^2)} = \sqrt{(5000 + 5000)} = \sqrt{10000} = 100 units

Step 4: The angle θ with respect to the x-axis is given by:
θ = tan^-1(R_y/R_x) = tan^-1(1) = 45º.

Therefore, the resultant vector R has a magnitude of 100 units and is inclined at an angle of 45º to the x-axis.