How do you draw the vector corresponding to a displacement 30 meters 30 degree south of east?

Answer 1

Even with the ample bundle of good information given in the question, we still

have a few questions to ask where there's some ambiguity, and therefore a few

assumptions to make in order to arrive at an answer:

-- Do you want an ordinary straight-line vector in 3-D Cartesian space, that dives

down into the globe near Cairo and pops up out of it again in the south Atlantic ?

Or do you want the navigation vector ... bearing and distance ... along the surface

of the earth ? We assumed the latter.

-- There are infinitely many paths available between two points on the surface of

the sphere. We assumed the minor (shorter) arc of the great-circle (shortest) path.

-- The direction is the easier part. For a good distance, we need a radius.

We used 3,959 statute miles.

So our vector, starting at 30

Answer 2

It all greatly depends on the further assumptions you make when solving the problem. Are you assuming your path is a straight line through 3-dimensional space(and therefore through the earth's surface) or are you assuming that the path lies on the sphere's surface? Also, what "perfect" radius would you assign to the earth due to it actually being an oblate spheroid? I assumed that your path lies on the surface of the earth. If you assign a coordinate system with it's origin at the starting point of 30N, 30E; and degrees for the corresponding cardinal directions are North = 0deg, East = 90deg, South = 180deg and so on, then in order to get to 30S, 30W, your heading would need to be SW at 225degrees. And then, assuming that the earth's radius is 3444 nautical miles, you would need to travel a distance of 5100.4 nautical miles (3444nmi*pi/180deg = 60.1 nmi/deg; 60deg latitude +60deg longitude = 84.853deg total (vector math)). Therefore, 5100.4 nmi @ a heading of 225deg.

Answer 3

Even with the ample bundle of good information given in the question, we still

have a few questions to ask where there's some ambiguity, and therefore a few

assumptions to make in order to arrive at an answer:

-- Do you want an ordinary straight-line vector in 3-D Cartesian space, that dives

down into the globe near Cairo and pops up out of it again in the south Atlantic ?

Or do you want the navigation vector ... bearing and distance ... along the surface

of the earth ? We assumed the latter.

-- There are infinitely many paths available between two points on the surface of

the sphere. We assumed the minor (shorter) arc of the great-circle (shortest) path.

-- The direction is the easier part. For a good distance, we need a radius.

We used 3,959 statute miles.

So our vector, starting at 30° N / 30° E and ending at 30° S / 30° W, is

5723.66 miles (9211.34 km) at bearing 229.1°

Answer 4

-- "30 degrees south of east" means:

> Face north.

> Turn 90 degrees to the right. You're facing east.

> Turn 30 more degrees to the right. You're facing 30 degrees south of east.

-- To construct that direction on paper, if you don't have a protractor:

> Mark the starting point.

> Measure 5 units to the right, and make a mark there.

> From that mark, measure 2.9 units down, and mark that spot.

> A line from the starting point to the last mark goes 30 degrees south of east.

-- To draw the vector:

> Draw a line 30 meters long, from the starting point through the last mark.

> Draw an arrow head on it, pointing away from the starting point.