## Description

Suppose that you plan to take a trip to your dream destination. You would like to know the shortest distance between your starting point and your destination. When calculating distances on a plane, you need only consider two dimensions because you are on a flat surface. However, when finding distances between two points on earth, you must take into the account the curvature of a sphere. In this portfolio, you will extend your knowledge of two-dimensional vectors to three-dimensional vectors in order to find the shortest distance between two points on the surface of earth.

### Unformatted Attachment Preview

Purchase answer to see full attachment

## Explanation & Answer

Attached you will find the answers of your task in Word and PDF format. The equations were made using the Microsoft Office Equation Editor. Please let me know if you need edits 😊

ANSWERS. PRECALCULUS. VECTORS.

PART 1.

Miami, Florida

x-coordinate:

𝑥 = cos(25.7671°) × cos(−80.1918°) = +0.15341

y-coordinate:

𝑦 = cos(25.7671°) × sin(−80.918°) = −0.88741

z-coordinate:

𝑧 = sin(25.7671°) = +0.43471

〈𝑥, 𝑦, 𝑧〉 = 〈+0.15341, −0.88741, +0.43471〉 = 〈𝑎, 𝑏, 𝑐〉

Anchorage, Alaska

x-coordinate:

𝑥 = cos(61.2181°) × cos(−149.9003°) = −0.41655

y-coordinate:

𝑦 = cos(61.2181°) × sin(−149.9003°) = −0.24146

z-coordinate:

𝑧 = sin(61.2181°) = +0.87646

〈𝑥, 𝑦, 𝑧〉 = 〈−0.41655, −0.24146, +0.87646〉 = 〈𝑑, 𝑒, 𝑓〉

PART 2.

‖〈𝑎, 𝑏, 𝑐〉‖ = √𝑎2 + 𝑏 2 + 𝑐 2 = √(0.15341)2 + (−0.88741)2 + (+0.43471)2 = 1.00000

‖〈𝑑, 𝑒, 𝑓〉‖ = √𝑑...

### Review

### Review

## 24/7 Homework Help

Stuck on a homework question? Our verified tutors can answer all questions, from basic **math** to **advanced rocket science**!

## Similar Content

## Related Tags

### My Brilliant Friend

by Elena Ferrante

### American Gods

by Neil Gaiman

### Harry Potter and the Sorcerers Stone

by J. K. Rowling

### Death Of A Salesmen

by Arthur Miller

### The Prince

by Niccolò Machiavelli

### East of Eden

by John Steinback

### The Handmaids Tale

by Margaret Atwood

### Things That Matter

by Charles Krauthammer

### Robinson Crusoe

by Daniel Defoe