1 2 Define an inner product on R² according to Let A -3 (u, v) Au · Av, where · denotes the usual dot product. Compute the distance between u = (1, –5) using this inner product. (3, 4) and v =

Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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Q: Let L be the line through the point Q = (-2, 9, -4) and direction vector -[-1, 2, -2]T. Find the two…

A: The equation of the line passing through the point x1, y1, z1 and having direction ratios l, m, n is…

Q: Find the cross product i x v where i = 2i +2j -3k and i = (- 8, – 6, 3). i x ở =

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Q: Use the dot product to determine whether v = 2i - 2j and w = -i + j are orthogonal.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: The transformation Po[1, ₂] = cos²0 cos sin cos sin sin²0 [1, ₂] onto the line through the origin…

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Q: Let the solid form in the orthogonal coordinate system xyz be surrounded by points A, B, C, D and F,…

A: The given co-ordinates of vertices are A = (-4, 1, 3), B = (6, 1, 1), C = ( 9, 5, 0), D = (4, 5, 1),…

Q: Find the cross product a x b. a = j + 6k, b = 3i - j + 5k Verify that it is orthogonal to both a and…

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Q: 4. Consider the vectors u,v and w are defined, u = 3i-j+4k, v = 4i – 2j +6k and w= 5i+2k (a) Express…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Evaluate (6x-3y)dA where Ris the parallelogram with vertices (2,0), (5,3), (6,7) and (3,4)using the…

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Q: Let v = (3, 0, 0) and w = (0, 1, −1). Determine u = v × w usingthe geometric properties of the cross…

A: Cross product: more formally called the vector product a way of multiplying two vectors and produces…

Q: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

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Q: Let u= (2,-3, 2, 5) and v a- i b- = (1, 2, 0, -4). Find scalars a and b so that au + bv = (0, -7,2,…

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Q: Calculate the cross product assuming that u x w = (6, 3, 6) (-u+3w) x w =

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Q: Find the cross product a x b. a=i-j-k, b=¹i+j+½ k Verify that it is orthogonal to both a and b. (a x…

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Q: Understand Properties of the Cross Product Given u x = (-4,-3, 4), find (u - 5v) × (ū+3v).

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Q: (2.) Let V be the vector space of M1x2(C) over R. (a.) Give a basis for V. (b.) Let W = { { 1] z €R.…

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Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

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Q: Find the condition for the points(a, 0).(h, k)(0, b) when ab 0 to be collinear.

A: When points are colllinear area should be 0Therefore, 12a01hk10b1=012ak1b1+1hkb1=0

Q: Let a and b be vectors in R?. (a.) Derive the area(2b + 5a, b – 2a) in terms of area(a, b). Explain…

A: Given: a,b∈ℝ2 If a=a1,a2 and b=b1,b2 then areaa,b=a1b2-a2b1. To do: Express the area2b+5a,b-2a in…

Q: Use the dot product to determine whether v = 5i - 5j and w = i - j are orthogonal.

A: Orthogonal vectors: Two vectors are orthogonal if there dot product is zero.

Q: Let ä(t) = (5, 4, 2)t + (-6, -4,1) and (u) = (-2, 1, 2)u+ (2, -8,-6). Find the acute angle between…

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