Ex. Prove the following identity (a x b) × (c x d) = (a · (b x d)) c – (a · (b x c)) d. %3D Hint: Use the contraction Sip dig eiklepgl Use Levi-Civita symbol and Kronecker delta to prove the vector identity.

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

Q: Find a unit vector e, where v = (1, 2, 3). ev

A: Unit vector is a vector that has magnitude 1 For a vector v=<x, y, z>Norm of vector v is…

Q: define: unit vector

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Q: 9. Given the vector ū =[-2,3,–4] a) Draw the vector. b) Determine a unit vector collinear with ū. y

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A: Given vector, u=3, 4, 5

Q: Which of these is a valid expression in index notation which outputs a vector? A d,F B © c) E F. F…

A: Given: Objective: Identify the valid expression in index notation that outputs a vector.

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A:

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Q: Question 8 Which vectors are in the span of B = w = w and x v and x

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A: To show that the magnitude of a vector does not change when we use the array  to rotate the vector…

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A: Given : length of vector b=35 ⇒b=35 Also, b makes angle 290° with positive x axis. So, b=b1i+b2j,…

Q: Let = ondu= a. Compute (ul. b. Compute +7. c. Compute 3u- 2 d. Compute e. Find o vector…

A:

Q: What is the resultant of vector A=2i +3j. and vector B=3i -2j Select one: a. 3.5 O b. 2 C. 5/2 Od.…

A: A vector is something that has both magnitude and direction. Like, if you are saying, someone is…

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Q: 5. Let a and b be vectors in R³. (a) Prove that a xb is orthogonal to both a and b (Note: It's…

A: Let a=a1 i +a2 j+a3k and b=b1 i +b2 j+b3k Then…

Q: Make all obvious simplifications.

A: We have to solve

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Q: In Cª, find a unit vector ū that is a positive real number multiple of z = (1 – i, i, 2, 3+ 4i).

A: Introduction: For a given complex vector z=z1,z2,...,zn, its length is formulated as…

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A:

Q: Let a be the vector of length 114 that when drawn in standard position makes a 165° angle with the…

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Q: (2.) Let V be the vector space of M1x2(C) over R. (a.) Give a basis for V. (b.) Let W = { { 1] z €R.…

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Q: 16. (2018) Let U and V be the points in R' with position vectors ū = (2, 1, 1, –2) and i = (3,0, –2,…

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