S F.d? = S.6 (o,0) F. 27- 3.2 then find (0,() If Fis a path-independent vector freld, with and So (1,4) 2.6 and (1,0) 1) (0,1) (1,0) c0,0)

Q: When the vector b = -2 is projected onto the line spanned by the vector a = 1 what is the error 2…

A: The projection of b onto a line spanned by a vector a is  b.a^=b.a|a| Given:  b=[-2-2-1]…

Q: 1. Consider the following vectors u, v, w ER?: --() -() --(E) (a) Represent the vector x = (-3, 4,…

A:

Q: 5. (a) Given A = a,5-ay2 + a₂, find the expression of a unit vector of B such that B/A and BL A, if…

A: Solution 5(a): Given that A→=5ax-2ay+az and  B→∥A→ if B→ lies in the xy-plane. So, B→=5bx-2by. Unit…

Q: For what value of m, the vector (m,3,1) a  linear combination of e\index{1}=(3,2,1) and…

A: We have to find the value of 'm' such that  is a linear combination of Assume

Q: 10. Find a unit vector in the same direction as PQ if P = (5, 4) and Q (3, 7). %3D

A: The solution is given as

Q: (15) Let u Then the angle (measured in radians) between these two vectors is equal to (b) (e) (d) 등…

A:

Q: Suppose f(x, y) = (1, -3). Then, (a) Vf(x, y) = (b) Vƒ(1,5) = (c) fu (1,5) = Du f(1,5) = x² + y² and…

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Q: o find the image of v and the preimage of w. , 2vq – v2 ), v = (1, 1), w = (-7/7, 2, -20) age of v…

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Q: In R, evaluate the alternating 2-form 5 = -3 · dx A dy on the pair of vectors (a, b) if a = (4, 2,…

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: (b) Consider the vectors u = (3,0) and 7 = (5,5). (i.) Find the size of the acute angle between u…

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Q: Use the function to find the image of v and the preimage of w. T(Vg, V2) = (V, + V2 V1 – V2), v =…

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Q: (-34,-9)and terminal pointQ-14 Given a vectorv with initial potnt the unit vectorstand i.

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Q: Q1. Consider the following vectors: -- () ---- () --C) 2 3 1 3 (a) Do the vectors i, u, w span R³?…

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Q: 11 1. 0 2 00 2 Find det(A) (14) Let A 3 00-1 (a) 0 (b) 6 (c) -6 (d) -2 (e) 2

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Q: Que. 1: Examine the following vectors for linear dependence X, =[1 2 4], X, = [2 -1 3], X, =[0 _1…

A: Write these vectors as rows in the matrix, convert the matrix to echelon form. If the echelon form…

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 V1, V1 + V2,…

A: Let us consider the transformation T: V→W defined as T(v)=w where v is preimage of w  and w is an…

Q: Use the function to find the image of v and the preimage of w. T(V₁ V₂ V3) = (4V₂ - V₁₁ 4V₁ +5V₂), v…

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Q: Use the function to find the image of v and the preimage of w. T(V₁ V₂ V3) = (V₂ - V₁ V₁ + V₂, 2v₁),…

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Q: O O O For which value of k the two vectors u=(3,k,-4) and v= (-4,8,1) are orthogonal? * None of…

A: Given  the two vector u = (3, k, -4) and v = (-4,8,1) we have to find for which value of k the two…