The direction ratios of the normal to the plane passing through (1, 0, 0), (0, 1, 0) which makes an angle of measure 45^ with the plane 2x + 3y = 7 are....

Step-by-step solution

Let the equation of the plane be ax + by + cz + d = 0 . Since the plane passes through (1, 0, 0) and (0, 1, 0) , we have: a + d = 0 a = -d b + d = 0 b = -d The direction ratios of the normal to the plane are (a, b, c) = (-d, -d, c) . Dividing by -d , the direction ratios can be written as (1, 1, k) , where k = - c d . The normal to the given plane 2x + 3y = 7 has direction ratios (2, 3, 0) . The angle between the planes is 45^ . Using the formula for the angle between two normals: 45^ = |1(2) + 1(3) + k(0)| 1^2 + 1