A question about vector notation

[Vioh]

Hi,

I am a little bit confused with how to use vector notation properly. For example, given point A (1, 2, 3) and B (4, 5, 6), then vector AB will obviously be (3, 3, 3). However, one of my friends told me that I have to write vector AB as a column vector. This is because (3, 3, 3) is the notation for a co-ordinate, rather than a vector. Is this true? and will I get marked down in an exam if i write (3, 3, 3) instead of a column vector?

Thanks!

[Abdelbari]

Hi,

I am a little bit confused with how to use vector notation properly. For example, given point A (1, 2, 3) and B (4, 5, 6), then vector AB will obviously be (3, 3, 3). However, one of my friends told me that I have to write vector AB as a column vector. This is because (3, 3, 3) is the notation for a co-ordinate, rather than a vector. Is this true? and will I get marked down in an exam if i write (3, 3, 3) instead of a column vector?

Thanks!

Both column vectors and unit vectors are correct... But if you choose a unit vector, then you should right 3i +3j +3k instead of (3, 3, 3)

[Vioh]

Oh, thank you Abdelbari. I see the difference now

[Abdelbari]

Your welcome Vioh

Edited May 9, 2014 by Abdelbari

[Rigel]

If you want to be more sophisticated, it is absolutely correct to name the vector as (3 3 3)^T (as in this case, it will be the transpose of the column vector, which is a matrix representation). You might want to use it if you want to save some space in exams, as answers can get easily messy dealing with vectors.

[Vioh]

If you want to be more sophisticated, it is absolutely correct to name the vector as (3 3 3)^T (as in this case, it will be the transpose of the column vector, which is a matrix representation). You might want to use it if you want to save some space in exams, as answers can get easily messy dealing with vectors.

Thanks, Rigel! It is really nice to use sophisticated notations, especially to save space in the exam. But is it fine to use this matrix representation without any understanding of it? because in this year syllabus, the IB has taken away everything about matrices, so I have no idea about this topic.

[Rigel]

If you want to be more sophisticated, it is absolutely correct to name the vector as (3 3 3)^T (as in this case, it will be the transpose of the column vector, which is a matrix representation). You might want to use it if you want to save some space in exams, as answers can get easily messy dealing with vectors.

Thanks, Rigel! It is really nice to use sophisticated notations, especially to save space in the exam. But is it fine to use this matrix representation without any understanding of it? because in this year syllabus, the IB has taken away everything about matrices, so I have no idea about this topic.

It isn't that complex of a concept (but it looks impressive the first time you see it). I doubt that they will give you any penalization for using that kind of notation (and it's just a quirk I guess to have proper mathematical notation). Say we have the following 2 x 2 matrix (let it be A):

(a c)

(b d)

Now, to get the transpose or A^T, we literally twist the elements around the "axis" formed by the elements in the main diagonal to then get:

(a b)

(c d)

As you see, the elements in the diagonal are left untouched. This can be applied to a 3 x 3 matrix as follows:

(a d g) (a b c)

(b e h) ----> (d e f)

(c f i) (g h i)

And now, we can extend this idea to n x 1 or 1 x m matrices as well (pardon the awkwardness of writing matrices in IBS, but it's kind of complicated to do).

[Vioh]

It isn't that complex of a concept (but it looks impressive the first time you see it). I doubt that they will give you any penalization for using that kind of notation (and it's just a quirk I guess to have proper mathematical notation). Say we have the following 2 x 2 matrix (let it be A):

(a c)

(b d)

Now, to get the transpose or A^T, we literally twist the elements around the "axis" formed by the elements in the main diagonal to then get:

(a b)

(c d)

As you see, the elements in the diagonal are left untouched. This can be applied to a 3 x 3 matrix as follows:

(a d g) (a b c)

(b e h) ----> (d e f)

(c f i) (g h i)

And now, we can extend this idea to n x 1 or 1 x m matrices as well (pardon the awkwardness of writing matrices in IBS, but it's kind of complicated to do).

Thanks again, Rigel! This surely looks like a very fun concept, and I'm definitely gonna use it considering the troubles of using column vectors (due to waste of space), and of using unit vectors (due to the annoying i, j, and k)

[elaifyanre]

If you want to be more sophisticated, it is absolutely correct to name the vector as (3 3 3)^T (as in this case, it will be the transpose of the column vector, which is a matrix representation). You might want to use it if you want to save some space in exams, as answers can get easily messy dealing with vectors.

Thanks, Rigel! It is really nice to use sophisticated notations, especially to save space in the exam. But is it fine to use this matrix representation without any understanding of it? because in this year syllabus, the IB has taken away everything about matrices, so I have no idea about this topic.

It isn't that complex of a concept (but it looks impressive the first time you see it). I doubt that they will give you any penalization for using that kind of notation (and it's just a quirk I guess to have proper mathematical notation). Say we have the following 2 x 2 matrix (let it be A):

(a c)

(b d)

Now, to get the transpose or A^T, we literally twist the elements around the "axis" formed by the elements in the main diagonal to then get:

(a b)

(c d)

As you see, the elements in the diagonal are left untouched. This can be applied to a 3 x 3 matrix as follows:

(a d g) (a b c)

(b e h) ----> (d e f)

(c f i) (g h i)

And now, we can extend this idea to n x 1 or 1 x m matrices as well (pardon the awkwardness of writing matrices in IBS, but it's kind of complicated to do).

See this link http://www.ibsurvival.com/topic/15583-quick-guide-to-maths-symbols-on-the-computer/ for help on typing math symbols.