We have three vectors u, v and w in R: 1 = U = (7a) Are these vectors ü, v and w linearly independent? Justify your answer. (7b Find a vector XE R* that is not in the span of ü, v and w. Make sure to provide an explanation of why x is not in the span of u, v and w.

Q: (2) Given u = [2 1 2]T, find a vector v so that the angle between u and v is 60° and the orthogonal…

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Q: (3) Suppose a vector x is orthogonal to vectors u and v. Show that x is orthogonal to u+v.

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A: What can be said about the vectors u and v when the eprojection of u onto v equals u?

Q: Find the vector component of u = ⟨5, 10⟩ that is orthogonal to v = ⟨4, 3⟩, given that…

A: Given,      w1 = projvu = ⟨8, 6⟩   and     u = ⟨5, 10⟩ = w1 + w2.      Where,  u = ⟨5, 10⟩ ,  v =…

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A: Given: v=1c. w=2-1 Vector v and w are orthogonal only if the dot product of vectors is zero.

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Q: Let v = 2i - 5j and w = i - j.Decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

A: v=2i-5j  and  w=i-j. Now, v·w=2i-5j·i-j=21+-5-1=2+5=7 & w=12+-12=2

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Q: 1. Show that the necessary and sufficient condition for two nonzero vectors A and B to be…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

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Q: If y is orthogonal to the vectors u and v, then y is orthogonal to u+ 3v. True False

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Q: Consider the vector v = (−1, 3, 0, 4). Find u such that (a) u has the same direction as v and…

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Q: Find the spacing and involution for the following vector functions 1- ƒ(x, y, z) = (xi + yj + zk]…

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Q: The vector is orthogonal to the plane 4x + 5y –7z =1 Select one: O True O False

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Q: 1 (b) Find the span of vectors i = |0 and j = |1 in R3

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Q: Let v = 2i - 5j and w = i - j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

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Q: Find a vector v parallel to the intersection of the planes 3x + y + 2z = 3 and – (x + 2y + 4z) = 7.

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Q: 1. Plot the following vectors using arrows on an xy-graph: -- (}). v-[+]. 1 u = V = 2u, u+v. Is…

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Q: We have three vectors u, v and w in R4: (7a)[6 marks] Are these vectors u, v and w linearly…

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Q: Evaluate 1+ x² + y*dS, where S is the helicoid with vector equation r(u, v) 0 < u < 2, 0 < v < 2T

A: Given ∬S1+x2+y2dS where S is the helicoid with ru,v=u cos v, usin v, v, 0≤u≤2, 0≤v≤2π. Since ru,v=u…

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Q: H.W 9- Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b %3D %3D…

A: Given: a→=1,1, b→=-1,0 To find: A vector in the same direction as but a→+b→ five times as long.

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Q: b) Find out the Vector =y²z?i+x?z?j+z²y²k is irrotational or not?

A: By definition, Any vector is said to be irrotational if the curl of the vector is zero. The given…

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Q: Given that u =, and z = What is the x component of the resultant vector w = Зи + 22

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Q: Q1. A- Find the cross product (uxv) of vector (u = i – 2j + 5k) and vector ( v=). Are the two…

A: Topic = Vector If the cross product of two vectors is zero it means both are parallel to each other.

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Q: Consider the vectors H [0] H . If I is the line defined by the vector w₁, fi W1 = [o] W2

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