Summer School Calculus

posted by Derek

I don't know how to answer this: A vector can be used to represent the path of a drill tip used to bore a deep mine shaft in Sudbury one quarter of the way to the centre of the Earth. Represent the vector using a directed line segment and Cartesian co-ordinates and describe which representation may be more suitable in this situation. Thanks a bunch!

1. drwls

If x,y,z are coordinates of the mine opening at a point on the surface of the Earth (radius R), then they satisfy x^2 + y^2 + z^2 = R^2.

In this case, the coordinates of the other end of the mine line segment are 0.75 x, 0.75 y, 0.75 z. That may satisy your "Cartesian representation" question.

If the vector from the center of the Earth to the mine opening is R (which should be in boldface type or with an arrow above to denote a vector), then (3/4) R is a vector denoting the tunnel line segment.

The second format appears more suitable.

Similar Questions

I don't know how to answer this: A vector can be used to represent the path of a drill tip used to bore a deep mine shaft in Sudbury one quarter of the way to the centre of the Earth. Represent the vector using a directed line segment …
2. URGENT: Calculus

I don't know how to answer this: A vector can be used to represent the path of a drill tip used to bore a deep mine shaft in Sudbury one quarter of the way to the centre of the Earth. Represent the vector using a directed line segment …
3. Physics

You are hiking out in California and come across an abandoned mine shaft. Wondering how deep the mine shaft is you toss a rock in and it takes 5.1 seconds before hitting the bottom. How deep is the mine shaft in meters?
4. physics

a stone is dropped from rest at the top of a mine shaft. it takes 59 s for a stone to fall to the bottom of a mine shaft. how deep is the shaft?
5. Calculus and vectors

A vector can be used to represent the path of a drill tip used to bore a deep mine shaft in Sudbury one quarter of the way to the centre of the Earth. Represent the vector using a directed line segment and Cartesian co-ordinates and …
6. physics

A stone is dropped from rest at the top of a mine shaft. It takes 58 s for a stone to fall to the bottom of a mine shaft. How deep is the shaft?
7. math

A vector can be used to represent the path of a drill tip used to bore a deep mine shaft in Sudbury one quarter of the way to the centre of the Earth. Represent the vector using a directed line segment and Cartesian co-ordinates and …
8. math

A vector can be used to represent the path of a drill tip used to bore a deep mine shaft in Sudbury one quarter of the way to the centre of the Earth. Represent the vector using a directed line segment and Cartesian co-ordinates and …
9. physics

It takes 5 seconds for a stone to fall to the bottom of a mine shaft. How deep is the shaft?
10. calculus

A cable that weighs 6 lb/ft is used to lift 750 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum.

More Similar Questions