Let u = (₁, ₂) and v = (v₁, V₂) be vectors in R². Consider an inner product in R2 defined by the formula (u, v) = 201₁ - U₁ V2 — U2V₁ + U2V2. i. Show that R²2 with the above defined inner product is a real inner product space. ii. Find the distance between vectors u = (2, 1) and v= (1,2) using the inner product defined above.

Q: Consider three vectors u = 3i +j+ ak, = 2i + bj +k, = -4i + (b – 2)3 + (b+ 8)k, where a and b are…

A: The solution are next step

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Q: 18) a) Find a unit vector that is orthogonal to both u = and v = . b) find the area of the…

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Q: Find the vector projection of v = -6i + 10j – konto w = = 2i + j − k (Give your answer using…

A: The given two vectors are  v=-6i+10j-k  and w=2i+j-k

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Q: Use the cross product to determine the angle between the vectors [4, 5, 2] and= [-2, 6, 1]. Verify 9…

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Q: Consider the three vectors u = (0, -2,3), v = (1,-4,0) and w=(-4,3,-5). a) Find the cross product…

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Q: Consider the points P(2,4,3) and Q (1, –5,2) in 3- space. Find the position vectors rī and rz for P…

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Q: Find the cross products of vectors: u=(0,-4,2) and v=(-3,2,6). Find the area of the parallelogram…

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Q: d) Check whether the given points P(2, -3, 4), Q(-1, 2, 3), R(0, 7, 1) are collinear or not. e) Find…

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Q: Suppose v1, v2, v3 is an orthogonal set of vectors in R°. Let w be a vector in Span(v1, v2, v3) such…

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Q: given u=5i+j+(a+2)k  and v= (3b-1)j +4j+ 6k  determine a,b so that v are parallel vectors

A: Given that, u=5i+j+(a+2)k  and v= (3b-1)j +4j+ 6k  We have to determine a,b so that u and v are…

Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

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Q: What is the definition of the triple scalar product for vectors u, v, and w in ℝ3?

A: To Define: Scalar Triple Product for vectors u, v and w in ℝ3.

Q: Find the value of a so that the vectors a = (11, −29, 13), b = (46, 5, 37), and c = (a, -194,-70)…

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Q: Express A = (3, 1, – 1) as B+ C, where B is parallel to the vector (1,4, 2) and C is perpendicular…

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Q: For the vectors u= (-8,0,3) and v= (1,3,-3), calculate proj,u and scalvu.

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Q: : (2,1,2). 1- Find the unit vectors u1 and u2 in the directions of v = (1,3) and w = Find unit…

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Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

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Q: Consider the two vectors u = 5i+j-4k and v=3i+j - 4k Find the cross product u x v. U XV= j+ k

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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: (a) AB-BC (b) projABAC (the vector projection of AC onto AB) (c) the area of AABC

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Q: Let ū = (3,2), v = (-2, –2), and w = (-4,3). Find the vector x that satisfies 5u – v +x = 7x + w. |…

A: Given that u→=3,2v→=-2,-2w⇀=-4,3