Express the given vector in terms of its coordinates

[robertjford80]

Homework Statement

Express the given vector in terms of its coordinates:

The vector from the origin to the end point of the vector from (-3,7,2) in the direction and with the length of u = (2, -3, 4)

The Attempt at a Solution

I don't even know the algorithm for solving this problem. Looking at the solution manual and the other questions it looks like you subtract the second vector from the first, so that would be

0 - -3 = 3
0 - 7 = -7
0 - 2 = -2

So the new vector is 3, -7, -2



Then, I'm just guessing that you subtract that from u

2 -3 = -1
3 - -7 = 10
4 - -2 = 6

The book says the answer is -1, 4, 6 so I'm almost right but it would be great to know the algorithm for how to solve these problems since the book is rather vague there.

 

[DryRun]

The vector from the origin to the end point of the vector from (-3,7,2) in the direction and with the length of u = (2, -3, 4)

Your question isn't very clear. Type it exactly as it appears in your book.

 

[robertjford80]

 

[tiny-tim]

hi robertjford80!

… the end point of the vector from (-3,7,2) in the direction and with the length of u = (2, -3, 4)

so that vector starts at (-3,7,2) and you add (2,-3,4) to it

(and you got a -3 instead of a 3)

 

[robertjford80]

ok, thanks.

 

[HallsofIvy]

Homework Statement

Express the given vector in terms of its coordinates:

The vector from the origin to the end point of the vector from (-3,7,2) in the direction and with the length of u = (2, -3, 4)

The vector "from (-3,7,2) in the direction and with the length of u = (2, -3, 4)" ends at the point (-3+ 2, 7+ (-3), 2+ 4)= (-1, 4, 6).

The Attempt at a Solution

I don't even know the algorithm for solving this problem. Looking at the solution manual and the other questions it looks like you subtract the second vector from the first, so that would be

0 - -3 = 3
0 - 7 = -7
0 - 2 = -2

So the new vector is 3, -7, -2
Then, I'm just guessing that you subtract that from u

2 -3 = -1
3 - -7 = 10
4 - -2 = 6

The book says the answer is -1, 4, 6 so I'm almost right but it would be great to know the algorithm for how to solve these problems since the book is rather vague there.

Frankly, I am concerned about your reference to knowing "the algorithm" and "just guessing". Knowing what these concepts mean, drawing a picture, and thinking about the problem should be your approach.

 

[robertjford80]

Frankly, I am concerned about your reference to knowing "the algorithm" and "just guessing". Knowing what these concepts mean, drawing a picture, and thinking about the problem should be your approach.

I'm concerned about it too. First learn how, then learn why. Learning why is five times harder than learning how. I went through about 6 chapters of calc before I really understood what a derivative was.

 

[tiny-tim]

… it would be great to know the algorithm for how to solve these problems …

i think your difficulty is with english, not with maths …

just read the question carefully, and you'll see that it tells you, in english, what maths to do …

"the vector from P and with the direction and length of u" means exactly what it says, start at P and add u

 

[robertjford80]

math is not English.

 

[tiny-tim]

yes it is!

every maths equation that you write (or read) should make perfect sense if translated carefully into english

 

[robertjford80]

if x requires translation than x is not english

 

[tiny-tim]

same language, different alphabet

(maths is like shorthand )

 

[HallsofIvy]

if x requires translation than x is not english

So if a person translates "Hamlet" into French then Hamlet was not in English to begin with? Here tiny-tim is referring to translating the problem, as given in English, to "mathematics".

Specifically, he is referring to your taking "vector from (-3,7,2) in the direction and with the length of u = (2, -3, 4)" and deciding that it should be written as (0- (-3), 0-7, 0-2) which is, in fact, the vector from (-3, 7, 2) to (0, 0, 0).

The "vector from (-3,7,2) in the direction and with the length of u = (2, -3, 4)" is (-3+ 2, 7+(-3), 2+ 4)= (-1, 4, 6). Notice, by the way, that (-3, 7, 2) is a point while (2, -3, 4) is a vector. I prefer to write vectors as <2, -3, 4> to make it easier to distinguish between points and vectors.