Prove that the planes (i) 12x – 15y + 16z – 28 = 0, (ii) 6x + 6y – 7z –8 = 0, and (üi) 2x + 35y - 39z + 92 = 0, have a common line of intersection. Prove that the point in %3D which the line 3 e-1 y z- 3 meets the third plane is %3D 1 | equidistant from other two planes.

-Analyze whether the planes are orthogonal π₁ = 2x+2y+2z+8 2=4x-2y-2z+9

Find an equation for the plane that passes through the point (3, −6, 7) and is perpendicular to theplanes 5x −2y + z −5 = 0 and 3x + 4y −z + 6 = 0. Please show all work.

The equation of a surface, with respect to an orthonormal coordinate system for three-dimensional space, is a3 – 13 – 4x1x2 – 4x1x3 = 1. Identify the type of surface, and find the least distance from a point on the surface to the origin.