The plane x 2 + y 3 + z 4 = 1 cuts the co-ordinate axes at the points A, B, C respectively. Then the area of triangle ABC is

Step-by-step solution

The equation of the plane is given by x 2 + y 3 + z 4 = 1 . The intercepts on the coordinate axes are a = 2 , b = 3 , and c = 4 . The coordinates of the points where the plane cuts the axes are A(2, 0, 0) , B(0, 3, 0) , and C(0, 0, 4) . The area of the triangle ABC can be found using the areas of its projections on the coordinate planes, denoted as _ xy , _ yz , and _ zx . _ xy = 1 2 ab = 1 2 (2)(3) = 3 _ yz = 1 2 bc = 1 2 (3)(4) = 6 _ zx = 1 2 ca = 1 2 (4)(2) = 4 The total area of the triangle is given by = _ xy ^