Introduction to Three Dimensional Geometry

Let A(x, y, z) be a point in xy-plane, which is equidistant from three points (0, 3, 2), (2, 0, 3) and (0, 0, 1). Let B = (1, 4, -1) and C = (2, 0, -2). Then among the statements (S1) : ABC is an isosceles right angled triangle, and (S2) : the area of ABC is 9 22,

1. both are false
2. only (S2) is true
3. only (S1) is true
4. both are true

Let P(x, y, z) be a point in the first octant, whose projection in the xy-plane is the point Q. Let OP = ; the angle between OQ and the positive x-axis be ; and the angle between OP and the positive z-axis be , where O is the origin. Then the distance of P from the x-axis is

1. 1 - 2 2
2. 1 + 2 2
3. 1 + 2 2
4. 1 - 2 2