Question 1: Doing 2 DFTs in one go Consider two length N vectors with real numbers in them-a, y ERN. Let's compose a new vector c = x+iy € C (assigning its real part from a and imaginary from y). Let C, X and Y be the DFT of c, z and y respectively. (i) Show that Ik Ck + CN-k 2 Ck-CN-k 2i and y=

Q: (3) Suppose a vector x is orthogonal to vectors u and v. Show that x is orthogonal to u+v.

A: We will use the fact that x is orthogonal to u and v to prove that x is orthogonal to u+v also

Q: 1. y -2+ 2.

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Q: Let ā= −i − 2j + 3k, b = i - 2j + 3k, c = −i +2j - 3k.

A: The given vectors .The objective is to find the vector that is perpendicular to both  and .

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Q: vectors i + cos (P- j+ cos (y - a) k, cos and s (ß−y) ĵ+ak, where a, ß and y are different angles.…

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A: Correct last vector coordinates representation

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A: None option is correct. The details solution of the given question is given below in step 2.

Q: Let a = 2i – j - 3k and b = 3i – j-k %3D (a) C ) Find two unit vectors orthogonal to both a – i and…

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Q: 5. Find the real part of the dot product of the vectors u" = (1 – i,1+ i) v° = (5+ i, –3 – i)

A: SOLUTION:

Q: Find a unit vector orthogonal to both u and v. u = 2i5j + 3k 2-3 V = + -k 10

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Q: Find the magnitude of the vector AB A=(4, 1) and B=(-3,0)

A: Given that, A = (4, 1) B = (-3, 0) We have to find the magnitude of the vector AB.

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A: In ℝ3, we have to evaluate the alternating 2-form ξ=-3·dx∧dy on the pair of vectors (a,b). a=4,2,12…

Q: 9. Let ū = (4, -6), T = (-2,4), and = (6,4). (a) Are ī and ū orthogonal vectors? How about ĩ and w?…

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