Math Problem Solver

In an orthonormal reference frame of space, we consider the point A(3: 1;-5) and the line d of parametric representation:

X= 2t+1

Y=-2t+9

Z = t-3

1. Determine a Cartesian equation of the plane P orthogonal to the line d and passing through point A.

2. Show that the point of intersection of the plane SP and the line d is the point B(5; -1).

3. Justify that the point C(7;3; -9) belongs to 9P, then show that ABC is an isosceles right triangle in A.

4. Let ‹ be a different real of 2 and M the parameter point / belonging to the line d.

A. Justify that the triangle ABM is a rectangle.

B. Show that the triangle ABM is isosceles in B if and only if the real r verifies the equation t^2- 4t = 0.

C. Deduce the coordinates of the points M, and M, of the line d such that the right triangles ABM, and ABM, are isosceles in B.