You are here:

# Advanced Math/Lines and planes in space

Question
I really have no clue what to do for this problem. I am extremely confused by the whole thing. It is the only problem left on my review package for my midterm this week. Thanks for any help.

A million years ago, an alien species built a vertical tower on a horizontal plane.

When they returned last week they discovered that the ground had tilted so that measurements of 3 points on the ground gave coordinates of (-2, 0, -5) , (3, -2, -3) and (-5, 5, -3).

a) What was the equation of the plane of the ground a million years ago?
b) Find the equation of the plane of the ground last week.
c) By what angle does the tower now deviate from the vertical? Tower now deviates by ______ radians."

Questioner:   Timothy
Private:   No
Subject:   planes word problem
Question:   I really have no clue what to do for this problem. I am extremely confused by the whole thing. It is the only problem left on my review package for my midterm this week. Thanks for any help.

A million years ago, an alien species built a vertical tower on a horizontal plane.

>>>> Then what was its normal vector?  What was an equation for a horizontal plane?
What does horizontal mean?

When they returned last week they discovered that the ground had tilted so that measurements of 3 points on the ground gave coordinates of (-2, 0, -5) , (3, -2, -3) and (-5, 5, -3).
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Can you compute two vectors IN the plane?
Can you compute the normal vector TO the plane?
Can you now write an equation for the plane?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
a) What was the equation of the plane of the ground a million years ago?
b) Find the equation of the plane of the ground last week.
c) By what angle does the tower now deviate from the vertical? Tower now deviates by

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Can you find the angle between the two normal vectors?

To you and all your 'friends' in Quebec:  I shall be on vacation from your questions for a while.  If you actually have a teacher, let him do his job.

Volunteer

#### Paul Klarreich

##### Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

##### Experience

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

Education/Credentials
-----------