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: The vectors u-(2,-1,1) and v= (1,1,2) in R3, the angle e between u and v is

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Q: Two vectors u and v in space are if and only if u X v= 0

A: Given vectors in space are u and v The vectors cross product is u x v = |u| * |v|* sin(angle between…

Q: What geometric relationship must two vectors have in order for ||u + v|| = ||u|| + ||v|| ?

A: The expression ∥u+v∥denotes the norm of u+v, ∥u∥denotes the norm of u and ∥v∥denotes the norm of v.…

Q: 1. Let v = PQ where P = (3,4,0) and Q = (2, 3, 1) Find a vector u that is parallel to V but with a…

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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: 1. Using the vectors u = [4, -3] 3 = [7, 1] and w = [-5, 3], evaluate the following, if possible. If…

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Q: Consider the vectors u=(2,3,-5), V = (-3, -2,6) and w=(-4,8,4). Calculate u.v

A: We have to find u.v

Q: If it is known that the internal product of the vectors ā (4, x, -2) and ƃ (1, x + 1,5) is 6,…

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Q: By using the multivariable chain rule, compute each of the following deriva- tives. (a) dz/dt and…

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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: The vectors į+j and i-į are perpendicular. True False

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

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Q: Let u=j-5k, v=5i-j+k, w=-10i+2j-2k Which vectors, if any, are perpendicular? Which are parallel

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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: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

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: Q3 O Let w-l(a,b,c), b= 3a} is Sub Sehoof RE a Sub Spaceef R32 is s w X, = i +2j - K , Xz= -3i+2j-R…

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Q: What domain makes sense for the function in this context?

A: Given g(t) = -16t2 + vt + h   Also initial velocity v = 80 ft/sec and launched of the ground so…

Q: If u, v are vectors such that |u || - 3, ||v|| - V5, and u v- 1, what is |u + v|| ?

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

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