7.8 Prove, by writing it out in component form, that (a × b) × c = (ac)b — (b. c)a, and deduce the result, stated in equation (7.25), that the operation of forming the vector product is non-associative.

Q: If u is a unit vector and a is a positive scalar satisfying au + = 0, find a and u.

A: Given: u is a unit vector and the scalar a is positive satisfying the equation au+1,-2,5=0 To find…

Q: c. Find the coordinate vector of the polynomial q(t)=3t² − 6t+2, relative to the basis for P₂ in…

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Q: Find vector c × (a + 3b), where a, b, and c are given below. ijk i j k -1 a = 509,b=0 0 1 0 -9i+27i…

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Q: Express the vector below in Cartesian coordinate: B = 2r sin cosc a₁ + r cose cose aer sind a ax=…

A: Given: The vector, B=2rsinθcosφar+rcosθcosφaθ-rsinφaφ   To express: The given vector in cartesian…

Q: Let v, w, and a be nonzero vectors such that v · a = w · a.Is it true that v = w? Either prove this…

A: Given: v, w and a is non zero vectors, such that: v·a=w·a To prove: v=w

Q: The figure shows a rectangular box in three- dimensional space that contains several vectors. (The…

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Q: Given that (A x B) x (C x D) = [A,C,D]B - [B,C,D]A, derive (A x B) x (C x D) = [A,B,D]C - [A,B,C]D…

A: To derive the second identity , assuming the truth of the first

Q: 11) Use properties of vector to determine the value of the dot product å. b for the vectors ở = 21…

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Q: Consider the 4-vectors Aª = (a, 0, 2a, 0) and Bª = (23, 0, 0, 0), where a and 3 are non-zero real…

A: and .It is given that  is null vector.

Q: Given ri = 3i - ej +In2 k, r2 = 5i + 7 e'j - 4 k and r3= 7i-7j+ k. Find the unit vector of (a)…

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Q: Q1: If , r₂ and r₂ are three parallel vectors of the same magnitude Prove that ₁+₂+3 is equally…

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Q: 8-b. Find the real part of the length of the vector v° = (5 + i, –2 + 2i, –1+i)

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Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: Find the vector ž, which is perpendicular to vectors å = (2,3, –1) and 5 = (1,–2,3) and satisfies…

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Q: Define first the scalar product of a row vector a and a column vector b, each having the same number…

A: The given matrices are,

Q: Let T: R2 R³ and u, v E R2 such that T(u) = 1 2 -2 and T(v) = 4 -2 1 Find the image under T of the…

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Q: 18 as a linear combination of = 8 Express the vector i and j =

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Q: Determine the scalar triple product u (v x w) of the vectors u = i + 2j + 3k; v= -i-j+k; w = i+j+k…

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Q: prove that 12 div A; = √√√x² {√8 8¹k Ax} = dxr div A¹, where A; and Ai are the covariant and…

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Q: Let V be the set of vectors shown below. v={[:] V= a. If u and v are in V, is u + v in V? Why? b.…

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Q: Given a = = 5e2 and b = 2e₁ + €3, let C = a b. If the tensor C operates on another vector d = 7e1…

A: Given vectors are written as follows.Given that .Given that  operates on a vector .We need to find…

Q: Find the coordinate vector of v = [-7 [-7 [011], [221] ). −4 -4 -5] relative to the ordered basis B…

A: Vβ​=[−3​0​−2​]   Explanation:

Q: Let a and b be vectors in R?. (a.) Derive the area(2b + 5a, b – 2a) in terms of area(a, b). Explain…

A: Given: a,b∈ℝ2 If a=a1,a2 and b=b1,b2 then areaa,b=a1b2-a2b1. To do: Express the area2b+5a,b-2a in…

Q: Prove: iv. if (x, y) = 0 for all x € R², then y must be the zero vector.

A: