# How do you express a vector in terms of I,J,&K?

nando94
Express the vector <1,0,0> in terms of I,J,&k.

(a)*I + (b)*J + (c)*K

You have to find a,b, and c. I know that I,J,&K are unit vectors and so I thought that a = 1, b = 0, c = 0. But the answer has radicals and fractions in it. I don't understand how to arrive at the solution.

## Answers and Replies

Mentor
If you know the supposed answer, why don't you post it here? This could help to understand where the difference comes from.

Which background (which course) does the question have?

Mentor
Express the vector <1,0,0> in terms of I,J,&k.

(a)*I + (b)*J + (c)*K

You have to find a,b, and c. I know that I,J,&K are unit vectors and so I thought that a = 1, b = 0, c = 0. But the answer has radicals and fractions in it. I don't understand how to arrive at the solution.

In terms of the unit vectors i, j, and k, <1, 0, 0> is 1i + 0j + 0k, or more simply, i. There shouldn't be any radicals or fractions.

nando94
Its part part of my homework for calc 3. I already tried 1,0,0 and it was wrong.

The problem gave a hint to do the dot product of the given vector with all the unit vectors. The previous problem was to express the vector <0,0,1> in terms of I,J&,K. The answer to that one was -sqrt(3)/2, 0,1/2. This one doesn't have answer in the back of the book and nothing in the chapter specifically talks about this problem.

Homework Helper
"i", "j", and "k" (small letters) are the unit vectors in the x, y, and z directions. Perhaps your "I", "J", and "K" (capital letters) mean something else?

Mentor
Hmm, I thought about quaternions, but that does not make sense here.
Unless I,J,K have some special definition given somewhere, I don't see how the result could be different from the one that you calculated in post 1.

Staff Emeritus
Perhaps your "I", "J", and "K" (capital letters) mean something else?
That was my thought as well, that these represent some other set of unit vectors other than the canonical i, j, and k, and that nando94 did not specify what these I, J, and K are.

nando94, what is the problem as written in the textbook, verbatim and in its entirety?

Homework Helper
Hmm, ##-\sqrt{3}/2## and 1/2 are typically sines and cosines of "nice" angles such as ##\pi / 6## and ##\pi / 3##.
But as said: we can keep guessing until you post more information, then we might be able to give you a conclusive answer.

nando94
The I,J,&K were vectors from a previous page that were supposed to be added together to result in <0,0,1>. I got the answer correct. Sorry for the confusion. This textbook is very unclear.

Mentor
The I,J,&K were vectors from a previous page that were supposed to be added together to result in <0,0,1>. I got the answer correct. Sorry for the confusion.
This is why we ask you to use the homework template, and post the complete problem statement. We were not able to read your mind that I, J, and K were given in the problem.
This textbook is very unclear.
That may be, but it doesn't help if you don't provide all of the given information.