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n-dimensional space - Wikipedia, the free encyclopedia - This is a 4 4 matrix that represents rotation at two speeds at once: See also. coordinate space; n-dimensional calculus; facet (mathematics) fourth dimension; four-vector..
N-dimensional space - In mathematics, an n-dimensional space is a topological space whose dimension is n (where n is a fixed natural number). The archetypical example is n-dimensional Euclidean space, which describes Euclidean geometry in n dimensions. n-dimensional spaces with large values of..
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Which solid can be represented as a three dimensional picture using th..
Which solid can be represented as a three dimensional picture using the figure and vector? => pyramid or sphere or cylinder or circle..
Position vector
. In addition to this, the direction of the position vector gives the direction q in which P lies, as observed from 0. It is important to note that position vectors are different for different positions of the particle. The above explanation can be extended to a three dimen..
. In addition to this, the direction of the position vector gives the direction q in which P lies, as observed from 0. It is important to note that position vectors are different for different positions of the particle. The above explanation can be extended to a three dimen..The figure M'N'O'P' is the image of MNOP. Describe the vector by using..
The figure M'N'O'P' is the image of MNOP. Describe the vector by using ordered pair notation. =><7, 7> or <- 3, - 7> or <7, 5> or <3, 7>..
Generalisation to N - Particles
>According to Newton's third law, For any a t h particle Substituting a = 1, 2,.. N. We have N equations. Adding them all, The position vector of the centre of mass of the whole system is given by, Where M = m 1 +m 2 +-------m N..
>According to Newton's third law, For any a t h particle Substituting a = 1, 2,.. N. We have N equations. Adding them all, The position vector of the centre of mass of the whole system is given by, Where M = m 1 +m 2 +-------m N..Question : Prove that F^(infinity) is infinite dimensional,
where F^(infinity) denotes the vector space consisting of all sequences of elements of real or complex numbers.
Answer : Assume that F has dimension n, which is a finite positive integer. Let a1 be the sequence starting with a 1 and all the other terms 0. Let a2 be a sequence of all zeros except the second term, which is 1. ... Let an be a sequence of all zeros except the n-th term, which is 1. Clearly, are linearly independent.
Now let's construct a sequence a(n+1) with all terms 0 except the (n+1)st, which is 1. Now, it's impossible to arrive at a(n+1) as a linear combination of , thus, the vector space cannot be n-dimensional for any positive integer n (proof by contradiction).
To Theodore: it can be proven that all vectors of an n-dimensional vector space can be written as linear combinations of ANY of the possible bases, so it follows that if a vector cannot be written as a linear combination of some basis then no other basis with n elements works.
Answer : Assume that F has dimension n, which is a finite positive integer. Let a1 be the sequence starting with a 1 and all the other terms 0. Let a2 be a sequence of all zeros except the second term, which is 1. ... Let an be a sequence of all zeros except the n-th term, which is 1. Clearly,
Question : How do you resolve three dimensional vectors?
Eg. [N 33 degrees E 44 degrees U]
Answer : I assume there is a comma between E and 44 and U means up Let V be the magnitude of the vector. i, j, k are unit vectors in x, y, z directions respectively The vector's projection in the x-y plane is Vcos44 90-33=57 That projection has components Vcos44[cos57 i + sin 57 j ] The projection of the vector on the z-axis is Vsin44 k So adding it up you have V{cos44*cos57 i + cos44*sin57 j + sin44 k }
Answer : I assume there is a comma between E and 44 and U means up Let V be the magnitude of the vector. i, j, k are unit vectors in x, y, z directions respectively The vector's projection in the x-y plane is Vcos44 90-33=57 That projection has components Vcos44[cos57 i + sin 57 j ] The projection of the vector on the z-axis is Vsin44 k So adding it up you have V{cos44*cos57 i + cos44*sin57 j + sin44 k }