Show that A*(BxC) = B*(CxA) = C*(AxB) Using the Levi Civita symbol (A,B,C are all vectors).
Show that A*(BxC) = B*(CxA) = C*(AxB) Using the Levi Civita symbol (A,B,C are all vectors).
1.15. Show the following vector identities by writing each vector in terms of Cartesian unit vectors and showing that each component of the LHS is equal to the corresponding component of the RHS. (a) a·(bxc)=c·(axb)=b·(cxa)
Prove using Levi-Civita veetors: (A × B) . (C x D) = (A-C)(B . D) _ (A-D)(B-C)
Prove using Levi-Civita veetors: (A)x B) . (C × D) = (A . C)(B . D) _ (A-D)(B-C) Jk
5. If bxc-iand axb- 2j+k, then what is (a - bc) x b?
4. You saw in class how the curl of a vector can be expressed using the Levi-Civita symbol. Another way to write the curl of a vector is as the deter- minant of a matrix with the basis vectors in the top row, partial derivatives in the second and vector components in the third. It should therefore not surprise you that the determinant of any 3 x 3 matrix can be written using the Levi-Civita symbol. a. Write the determinant...
first picture is the notation on the test paper Second picture is the question i would like to solve thanks~ Notation and convention: r x +y The distance from the origin to the point r [x,y,z] + ê: The unit vector along the direction of r-[x, y,z] (a.e,6)-i.j.):m :The orthonormal bases of a Cartesian coordinate system. for dummy indices Einstein convention: Omitting the summation notation (repeated indices). Examples:ab,-a b, ab a b Notice: No dummy index is allowed to be...
detailed work pls axb. Find the angle Let a, b 0 be vectors in R3 with angle between them #/7, and e 3. between each pair of vectors: c and b c and b x a b and b x c a and b x c axcand b xc detailed work pls axb. Find the angle Let a, b 0 be vectors in R3 with angle between them #/7, and e 3. between each pair of vectors: c and b...
QUESTION 7 t0 points Factors A, B, C D, E and interactions AxB, AxC, AxD, AxE, BxC, BxD, BxE CxD, CxE, DxE a. L4 b.L8 dL16 10 points QUESTION & DxE) how many columns minimum would be required (based on the L'n formulal) Oa 13 b.18 O d. 10 points QUESTION 9 n True True O False 10points QUESTION 10 QUESTION 7 t0 points Factors A, B, C D, E and interactions AxB, AxC, AxD, AxE, BxC, BxD, BxE CxD,...
1. Given the following 3 vectors, evaluate a. 2A+B b. C-A c. 2BXC-omit d. C-(AXB) - Ort A = 2i - 13 + 4k B=4i + ij - 5k C = -2i+2j – 3k = 120 at 450 - 200 at 1260 Find D E 2. The position of an object is related to time by X = Ata--Bt + C, where A -6m/s?.
Prove the following vector identity using index notation A X (BXC) = (A.C)B - (A.B)C