If the plane r = ( + ) i + (2 + ) j + (3 + 2 ) k , where and are parameters, intersects coordinate axes at points (a, 0, 0) , (0, b, 0) and (0, 0, c) then a + b + c = ...

Step-by-step solution

The parametric equations of the plane are given by: x = + y = 2 + z = 3 + 2 From the second equation, we have = y - 2 . Substituting into the first equation: x = + y - 2 = x - y + 2 Now, substituting both and into the third equation to eliminate the parameters: z = 3(x - y + 2) + 2(y - 2) z = 3x - 3y + 6 + 2y - 4 z = 3x - y + 2 Rearranging this, we get the Cartesian equation of the plane: 3x - y - z + 2 = 0 To find the x -intercept a , put y = 0 and z = 0 : 3a - 0 - 0 + 2 = 0 a = - 2 3 To find the y -intercept b ,