One of the questions on my Algebra assignment is as follows.
I don't need the answers, but need to understand how the helicopter takes its coordinates. I really don't understand the question itself, not the material.
An air traﬃc control tower Q records the location of planes nearby with
respect to a coordinate system e1 = (1, 0, 0), e2 = (0, 1, 0), e3 = (0, 0, 1),
where e3 is vertical. A helicopter R ﬂying near Q also measures the location of itself and other aircraft using the base of the tower as a base
point. It measures coordinates against its own height in the direction of
the vertical tower Q, its own displacement from Q, and the length l of
it’s propeller blade, parallel to the ground and perpendicular its displacement as measured along the ground. If at time t the helicopter R is at
(f(t), g(t), h(t)) as measured by the tower Q, ﬁnd the three coordinate
vectors R is using in terms of those that Q is using. Will these always
give a basis? Why?
What does R think its position is? Find the change of basis matrix from
R’s measurements to Q’s (for times t when it is a basis).
The Attempt at a Solution
I'm not sure where to start...