Let R2 have the weighted Euclidean inner product < u,v>= 3u₁v₁ + 4u₂v2, and let u = [1, 2], v = [-1, 2], w = [3,-1], and k = 2. Compute the stated quantities. a) b) c) d) ||v|| d(u, v)

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A: (a) Find u→+v→ as follows: u→+v→=-1,2,4+-3,5,2          =-1+-3,2+5,4+2          =-4,7,6

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Q: 25. Show that |v|u + Ju|v and |v|u – |u| v are orthogonal.

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A: Given the following six points in ℝ2. A1=(1,0), A2=(3,0) , A3=(2,3) , B1=(0,3) , B2=(3,2), B3=(0,1)…

Q: • r : (x, Y, z) = (7, 8, 2) + X(-3, –8, 2) %3D 7 – x y – 8 - x y – 8 2 – z • S : -7 -6 4

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A: As we know a×b = - b×a

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A: Given: u=1,1,1, v=2,1,0, w=0,0,1 we know that scaler triple product S.T.P. of given three vectors…

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Q: 9. Let A=span{v = (-1,–1,2), i = Projau. (2,3,0)} and w (1,2, 3). Find

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Q: U= 2i-35 j V = 59 +3

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Q: = [4, 3, 0] v = [-2,0, –3] u = u x v = Ex: 5 Ex: 5 Ex: 5

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Q: Find the area of parallelogram ABCD with vertice A(7,5,2), B(-1,2,9), C(6, –3, -4) and D(5,7,3).…

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Q: 21. Given vectors u = (1,3) and v = (-6,2). a) Find u - 3v b) Find Ju + v].

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Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

Q: Let r E R and --(), v- (), -- (1). 3 u = V = W = 2 For which values r ER is the set {u, v, w}…

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