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

In summary: If you don't do this you are not telling us the complete problem. In summary, the conversation discusses a problem in which the vector <1,0,0> needs to be expressed in terms of the unit vectors I, J, and K. The question also provides a hint to find the dot product of the given vector with all the unit vectors. However, there is confusion about the answer as the expected result does not match the calculated one. The conversation also mentions a previous problem where <0,0,1> needed to be expressed in terms of I, J, and K, and the correct answer was obtained. However, the textbook is considered unclear as it does not provide enough information for the problem. The conversation concludes with
  • #1
nando94
33
0
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.
 
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  • #2
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?
 
  • #3
nando94 said:
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.
 
  • #4
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.
 
  • #5
"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?
 
  • #6
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.
 
  • #7
HallsofIvy said:
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?
 
  • #8
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.
 
  • #9
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.
 
  • #10
nando94 said:
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.
nando94 said:
This textbook is very unclear.
That may be, but it doesn't help if you don't provide all of the given information.
 
  • #11
That teaches you the important fact that giving just three components of a vector doesn't tell you anything, if you don't tell wrt. which basis these components are taken. Further you also need to tell us the new basis vectors I, J, K.
 

1. How do I express a vector in terms of I, J, and K?

To express a vector in terms of I, J, and K, you can use the following formula: Vector = aI + bJ + cK, where a, b, and c are the magnitude of the vector in the x, y, and z directions respectively.

2. What do I need to know to express a vector in terms of I, J, and K?

In order to express a vector in terms of I, J, and K, you need to know the magnitude of the vector, as well as the direction it is pointing in. This information can be represented as a set of three numbers (a, b, c) in the formula: Vector = aI + bJ + cK.

3. Can a vector be expressed in terms of I, J, and K in any direction?

Yes, a vector can be expressed in terms of I, J, and K in any direction. This is because the direction of a vector is determined by the values of a, b, and c, while the magnitude is determined by the length of these values. Therefore, by varying the values of a, b, and c, you can express a vector in any direction.

4. How do I interpret the values of I, J, and K in a vector expression?

The values of I, J, and K in a vector expression represent the coefficients or scalars of the vector in the x, y, and z directions respectively. These values tell you how much the vector is pointing in each direction and can be used to calculate the magnitude and direction of the vector.

5. Can I express a vector in terms of other variables instead of I, J, and K?

Yes, you can express a vector in terms of any set of variables, as long as they represent the magnitude and direction of the vector. However, I, J, and K are commonly used as they represent the standard unit vectors in the x, y, and z directions respectively, and make vector calculations more straightforward.

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