Show that if u, v, w, and r are any vectors, then a) u x (v x w) + v × (w × u) + w × (u x v) = 0 b) u x v = (u·v ×i)i+ (u · v ×j)j+(u · v × k)k ju•W c) (u x v) · (w × r) = . u.r V•r

Q: Let =(5,4,1),(3,-4, 1), w=(1, -2, 3). Which pair of vectors, if any, are perpendicular (orthogonal)?…

A: We have to find out solution

Q: Let u, v, w be vectors. Which of the followings are meaningless? (Hint: The notation x means cross…

A: Use the actual meaning of vector and dot products.

Q: Which of the following pairs of vectors are perpendicular to each other? a) (4, 14, -18) and (6, 21,…

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Q: If v = –i + 2j and --Projw= w = -2i + 3k, then - اخترأحد الخيارات -9 52+ j.A C 2 .B - C. Zero vector…

A: Solution

Q: 3. Given (3, 10,-8) and v = (-1,6,4), b) find a unit vector in the same direction as v-u

A: The given problem is to find the unit vector in the same direction of the vector v-u. Given vectors…

Q: What if the vector v was [ 7, 11, 3]

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Q: 4. Given vectors: =(4,9), v = (-8, 15) and w=(2, 10) a) Show that and w can span R².

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Q: If some p vectors can span V, then dim V= p True False

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Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select…

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Q: 2. Let a, b and c be vectors in R". Prove that (a) a and (a c)b - (a - b)c are perpendicular; a b…

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Q: Express v = ⟨5, −3, 2⟩ as a sum of orthogonal vectors such that one of the vectors has the same…

A: Given that v = ⟨5, −3, 2⟩u = ⟨1, 1, −8⟩

Q: Q1: You have the following vectors: U= 6 2 4 V= 3 -2 3 0 3 W = -4 Z- 2 2 2 Which of the vector…

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Q: u * v =( u1v1, UzV2 , Uz V3 , · Un Vn).

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Q: Let u = (3, 6, 2), v = - (6, 7, -2), w = (24, 33, h + 0). Determine the value for h so that w is in…

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Q: 5. Let A = (4,3), B = (0, 1), and C = (−3, 7). (a) Find the vectors AB, BC, and AT. (b) Prove that…

A: Step 1:It is provided that, A=(4,3),B=(0,1), and C=(−3,7). (a) Then, it is obtained:AB=B−A…

Q: The cross product (u x v) of the two vectors u = i-2j + k and v = 3i + j - 2k is -3i - 5j7k. True

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Q: Let a and b be two unit vectors. 1) a x (a.b) 2) a . (axb) 3) a . (a+(axb)) 4) (axb) + (bxa)…

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Q: 3. Determine whether the vectors u and v are orthogonal, parallel or neither. (show/explain your…

A: (a). Given ,  u = 2,3,-1 and v = -1,-1,-1 (b). Given , u = j + 6k and v = i - 2j -k

Q: Let us consider two vectors in R³: u = (2, -3,5) v = (a, b, c) Find the values of a, b, and c such…

A: Two vectors are orthogonal if their dot product is zero.The dot product of two vectors u→=⟨u1,u2,u3⟩…

Q: Find the angle between the given vectors:  a) u=(3,4), v=(5,-12); = x1y1 +x2y2 b) u(1,1,1),…

A: Sol:- a) u=(3,4), v=(5,-12); <u,v> = x1y1 +x2y2 i.e a)  u=(3,4,0), v=(5,-12,0); <u,v> =…

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: Let z, w e C. Clearly prove that z+w = z + w.

A: Since you have asked multiple question , we will solve the first question for you. If you want any…

Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: Let W be the set of all vectors of the form 111 ū= -3s- 2t 2s+t -s-2t Find vectors u and 7 in R³…

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Q: Let a, b, and c be vectors. Is it a vector, scalar, or is in meaningless? 1) ( a X b ) + a.b 2) -2 +…

A: We will whether the part 1, 2 and 3 are a vector or a scalar or meaningless as following.

Q: For what value(s) of k are the vectors ü (2k, 5, k) and v = (3, -8, k) perpendicular

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