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

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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: 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: 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: 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: 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