Which of the following sets form bases: ) (1,1),(-1,1) for R² (1,2,1),(-1,2,1),(0,4,2) for R³ (1,1,1), (1,1,0), (1,0,0) for R³ (1,0,0), (0,2,0), (0,0,3) for R³

Q: Find the cross product a × b. a = (9, 0, -4), b = (0, 8, 0) Verify that it is orthogonal to both a…

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Q: u= , v=  , w= t is a real number find t so that u,v and w are coplanar

A: Since u, v and w are coplanar, so their scalar triple product is zero, that is  w.[uxv]=0 u x v:…

Q: Let →a=a→= and →b=b→=. Find kk so that →aa→ and →bb→ will be orthogonal (form a 90 degree angle).…

A: We Know that, Two vectors u and v are said to be orthogonal vectors if and only if u . v=0 Here, a =…

Q: 4. Prove that the vectors a= (1,1,1); b-(1,-1,0) and e-(-1,-1.2) are orthogonal to each other! 5.…

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Q: Let u = (3, 2, x) and v = (2x, 4, x). (a) Find all possible values of x that make u and v…

A: Given thata)We have to find all possible values of x that make u and v orthogonal.b)We have to find…

Q: Find 3 different homogeneous coordinate representations for the Cartesian point (1,-2)

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Q: Find the projection of u = onto v = .

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Q: Find the center of 8x 2 + 6y 2 - 32x + 24y + 8 = 0. (2, 2) (-2, 2) (2, -2)

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Q: Find the intersection of the line x = -1 + 2t, y = 3 + t, z = 4 - t with the yz-plane. O (1, -3, -4)…

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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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: Which of the following is not a plane? OF- (1,3,4) + s(2,-1,2) + (1,1,1), s,t e R O-(2,4,2) +…

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Q: 6. Determine if the vectors à = [−1, 5, 3], b = [−2, 4, 7], and ₹ = [10,7,1] ar are coplanar.

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Q: Find a linear map T that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

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Q: Which of the following is a point on the plane with equation n = (-3, -2, 2) + t(2, 2, -2) + s(1,…

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