Use the determinant to compute the area of the parallelogram induced by the following two vectors: 6.2 01 = [6²4] -3.4 Area Number -5.1 .62 = [32].

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: Find the cross product a × b. a = j + 9k,    b = 4i − j + 2k       Verify that it is orthogonal…

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Q: b) Heron's Formula Area = √5(5-a)(s-b)(s-c), where s = 1/(a+b+c) prove using the following steps.

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Q: If z = 1+ 2i and w = 3+ 4i, express the following in the rectangular form: (a) 2|w| +(1 – i)2² w + z…

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Q: Evaluate ( 3+j4)( 3+j4) = A +jB, determine the real component A

A: Given,              (3+j4)(3+j4)=A+jB

Q: 1. Calculate the area of the parallelogram spanned by the vectors Á = and B = .

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Q: If z1 = 3 + j2 and z2 = 5 – j3 , what is the simplified form of z1 z2 ?

A: We know that the rectangular form of a complex number is written as z=a+jb where a and b are real…

Q: 3. Express (j-3)° in rectangular form.

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Let x=x= and y=y= Find the dot product of xx and yy.     x⋅y=x⋅y

A: Given:x=9, 0y=-4, -2Dot product:A=ax ,ay  B=bx ,byAB=axbx,+ay,by

Q: - - Find the cross product (-2i - j + k) × (3i − j − k). Answer:

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Q: Use the adjoint of A to find A−1, where

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Q: Find the dot product: (5, —3) о (2, 3) O 1 O -1

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Q: Evalute ) (2xty)dA, where D=2C2-1にと」 225y41tX)

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Q: Find the cross product a x b. a = j + 6k, b = 3i - j + 5k Verify that it is orthogonal to both a and…

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Q: Compute: 19 (4-2i)(4+2i)

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Q: Evaluate (6x-3y)dA where Ris the parallelogram with vertices (2,0), (5,3), (6,7) and (3,4)using the…

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Q: if complex numbers Z1= 4.5-j5.1 , Z2= 3.2- j6.2, Z3= 2.25-j5.6 , Z4= 7.5-j9.2 , then calculate…

A: Given complex numbers are…

Q: Given the points (-1, 3), (0, 1), (1, 3), and (2, 9), solve the equation Ax = b for x = c de to find…

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Q: Let u = 10i + 2j, v=i+j, and w = i-j. Find scalars a and b such that u = av + bw. a = b =

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Q: Cakulate (3i+2j+k) • (i + zj - k

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Q: Express (-2/3+ j2) in rectangular form.

A: Rectangular form of the given complex number

Q: Find the distance d (in the complex plane) between z = 2 + 7i and w = 11 - 10 i. d = √ (1)² + (9)² X

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Q: Given u⃗ =⟨2,−5⟩ and v⃗ =⟨4,−4⟩, find the dot product u⃗

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Q: 3) If a = 31-2j, b = 7i+5j and c = 9i-j, show that a - (b-c) = (a - b) - (a - c). %3D

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Q: Q) Verify that (bx с) %3D b.(с х а) — с. (а x b) if a %34i — 3ј +6k , b- 5i +4j — 3k, с %3 4i +6j +3…

A: Given the three vectors

Q: Compute the order of each element in the Quaternions, Q8. Show your work.

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Q: Express −i+j in the form [a,b]

A: Simplification