Assessment: Analytic Solid Geometry

How many coordinates are needed to describe a point in three-dimensional space?

Find the distance between (0,0,0) and (3,4,12).

Find the direction number "a" for the line through (1,1,1) and (7,3,9).

For the parametric line x=1+2t, y=3−t, z=4+5t, find the x-coordinate at t=2.

Find d, for the plane through (1,0,2) with normal vector (2,3,1), written as 2x+3y+z=d.

A sphere has center (0,0,0) and radius 6. What is the right-hand side of its equation x²+y²+z²=?

A drone's flight-planning software calculates how close the drone will pass to a flat rooftop, modeled as a plane. Which technique gives this directly?

Engineers are given a satellite's signal-coverage sphere as an expanded (non-standard) equation and need its actual center and radius. What technique finds these?

Find the midpoint's y-coordinate for A(−3,7,2) and B(9,−1,10).

A plane has equation 6x+8y+0z=50. Find the distance from the origin to this plane.