Let a and b be vectors in R?. (a.) Derive the area(2b + 5a, b – 2a) in terms of area(a, b). Explain which property is used in every step of derivation. (b.) Let a = (a1, a2) and b = (b1,b2). The area(a, b) is given by aıb2 - azb1. Compute the area in (a.) when a = (3, -2) and b = (1,1).

Q: Find the dot product of x = 5 and y = 0 x.ÿ= 2 ི ༠༠

A: Step 1:Given to find the dot product.For vectors of form ⎣⎢⎡​x1​x2​x3​​⎦⎥⎤​ and…

Q: Use the dot product to determine whether v = i + j and w = -i + j are orthogonal.

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Q: Calculate v × w. v = 〈2, 0, 0〉, w = 〈-1, 0, 1〉

A: Given vectors are v=2, 0, 0 and w=-1, 0, 1. To calculate: v×w Solution: Given vectors can be written…

Q: Use the dot product to determine whether v = 5i and w = -6j are orthogonal.

A: Given:

Q: B: 1. Find (1+ i)* 2. Find the area between the vectors A = 2i – 2j + k , B = 3i + 4k

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Q: Evaluate into rectangular form 2 = 15 + j8 4+j 4. 4+j

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Q: Calculate the dot product, of u and v, where u = 58 î - 75 ĵ + 12 k and 34 Î – 73 ĵ - 97 k. = u.v=

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Q: Use the dot product to determine whether v = 2i - 2j and w = -i + j are orthogonal.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Use the dot product to determine whether v = 5i and w = -6i are orthogonal.

A: The given vector is v=5i  and  w=6i known fact: Two vectors a and b are orthogonal (perpendicular)…

Q: Find the dot product 9) v = 12i + 9j, w = -10i – 8j

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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: Use the dot product to determine whether v = 3i and w = -4i are orthogonal.

A: Let "." represent the dot product Dot product = v.w Two vectors u and v whose dot product is u·v=0…

Q: Find the angle a in radians between the vectors απ -3] and

A: Step 1: Given vectors: u=[−3−1​] and v=[1−2​] Step 2: To find the angle 𝛼 between two vectors a and…

Q: What conditions on a column vector u will make ulu zero? T

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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: Use the dot product to determine whether v = 5i - 5j and w = i - j are orthogonal.

A: Orthogonal vectors: Two vectors are orthogonal if there dot product is zero.

Q: Use the dot product to determine whether v = 2i + 8j and w = 4i - j are orthogonal.

A: Given: v=2i+8jw=4i-j

Q: Let v = (5, 8) and w = (4, 5). What is the dot product v · w?

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Q: 9. Simplify each vector operation. a) j-(-)) ī b) (ixj).k 1 c) (ixj)xk ī

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Q: Can it be fit diagonally ?

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