Let v = (-1,3,4). Find (a) a unit vector in the direction. of v and (b) a unit vector in the opposite direction
Let v = (-1,3,4). Find (a) a unit vector in the direction. of v and (b) a unit vector in the opposite direction
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let v = (-1,3,4). Find (a) a unit vector in the direction
of v and (b) a unit vector in the opposite direction
Expert Solution
Step 1: Given the information
The given vector format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%40font-face%7Bfont-family%3A'round_brackets18549f92a457f2409'%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMjwHLFQAAADMAAAATmNtYXDf7xCrAAABHAAAADxjdnQgBAkDLgAAAVgAAAASZ2x5ZmAOz2cAAAFsAAABJGhlYWQOKih8AAACkAAAADZoaGVhCvgVwgAAAsgAAAAkaG10eCA6AAIAAALsAAAADGxvY2EAAARLAAAC%2BAAAABBtYXhwBIgEWQAAAwgAAAAgbmFtZXHR30MAAAMoAAACOXBvc3QDogHPAAAFZAAAACBwcmVwupWEAAAABYQAAAAHAAAGcgGQAAUAAAgACAAAAAAACAAIAAAAAAAAAQIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAo8AMGe%2F57AAAHPgGyAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACgAAAAGAAQAAQACACgAKf%2F%2FAAAAKAAp%2F%2F%2F%2F2f%2FZAAEAAAAAAAAAAAFUAFYBAAAsAKgDgAAyAAcAAAACAAAAKgDVA1UAAwAHAAA1MxEjEyMRM9XVq4CAKgMr%2FQAC1QABAAD%2B0AIgBtAACQBNGAGwChCwA9SwAxCwAtSwChCwBdSwBRCwANSwAxCwBzywAhCwCDwAsAoQsAPUsAMQsAfUsAoQsAXUsAoQsADUsAMQsAI8sAcQsAg8MTAREAEzABEQASMAAZCQ%2FnABkJD%2BcALQ%2FZD%2BcAGQAnACcAGQ%2FnAAAQAA%2FtACIAbQAAkATRgBsAoQsAPUsAMQsALUsAoQsAXUsAUQsADUsAMQsAc8sAIQsAg8ALAKELAD1LADELAH1LAKELAF1LAKELAA1LADELACPLAHELAIPDEwARABIwAREAEzAAIg%2FnCQAZD%2BcJABkALQ%2FZD%2BcAGQAnACcAGQ%2FnAAAQAAAAEAAPW2NYFfDzz1AAMIAP%2F%2F%2F%2F%2FVre7u%2F%2F%2F%2F%2F9Wt7u4AAP7QA7cG0AAAAAoAAgABAAAAAAABAAAHPv5OAAAXcAAA%2F%2F4DtwABAAAAAAAAAAAAAAAAAAAAAwDVAAACIAAAAiAAAAAAAAAAAAAkAAAAowAAASQAAQAAAAMACgACAAAAAAACAIAEAAAAAAAEAABNAAAAAAAAABUBAgAAAAAAAAABAD4AAAAAAAAAAAACAA4APgAAAAAAAAADAFwATAAAAAAAAAAEAD4AqAAAAAAAAAAFABYA5gAAAAAAAAAGAB8A%2FAAAAAAAAAAIABwBGwABAAAAAAABAD4AAAABAAAAAAACAA4APgABAAAAAAADAFwATAABAAAAAAAEAD4AqAABAAAAAAAFABYA5gABAAAAAAAGAB8A%2FAABAAAAAAAIABwBGwADAAEECQABAD4AAAADAAEECQACAA4APgADAAEECQADAFwATAADAAEECQAEAD4AqAADAAEECQAFABYA5gADAAEECQAGAB8A%2FAADAAEECQAIABwBGwBSAG8AdQBuAGQAIABiAHIAYQBjAGsAZQB0AHMAIAB3AGkAdABoACAAYQBzAGMAZQBuAHQAIAAxADgANQA0AFIAZQBnAHUAbABhAHIATQBhAHQAaABzACAARgBvAHIAIABNAG8AcgBlACAAUgBvAHUAbgBkACAAYgByAGEAYwBrAGUAdABzACAAdwBpAHQAaAAgAGEAcwBjAGUAbgB0ACAAMQA4ADUANABSAG8AdQBuAGQAIABiAHIAYQBjAGsAZQB0AHMAIAB3AGkAdABoACAAYQBzAGMAZQBuAHQAIAAxADgANQA0AFYAZQByAHMAaQBvAG4AIAAyAC4AMFJvdW5kX2JyYWNrZXRzX3dpdGhfYXNjZW50XzE4NTQATQBhAHQAaABzACAARgBvAHIAIABNAG8AcgBlAAAAAAMAAAAAAAADnwHPAAAAAAAAAAAAAAAAAAAAAAAAAAC5B%2F8AAY2FAA%3D%3D)format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%224.5%22%20y%3D%2216%22%3Ev%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2217.5%22%20y%3D%2216%22%3E%3D%3C%2Ftext%3E%3Ctext%20font-family%3D%22round_brackets18549f92a457f2409%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2229.5%22%20y%3D%2216%22%3E(%3C%2Ftext%3E%3Ctext%20font-family%3D%22round_brackets18549f92a457f2409%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2291.5%22%20y%3D%2216%22%3E)%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2237.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2248.5%22%20y%3D%2216%22%3E1%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2255.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2266.5%22%20y%3D%2216%22%3E3%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1c3eabe56388c5f9cb7de19517e%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2273.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2284.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3C%2Fsvg%3E)
.
The aim is to find the unit vector in the direction of 
and the unit vector in the opposite direction of .
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