In which of the following cases is the mapping x: R² → R³a patch? (а) x(и, v) — (и, uv, v). (c) x(и, v) — (и, и?, у + r'). (b) x(и, v) — (и", и", v). (d) х(и, v) — (сos 2ли, sin 2ли, v).

Q: 5. a) What is the orthogonal projection ŷ, of y = (2) U = and the origin? -3 9 onto the line (L)…

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Q: Let (l, m, n,), i = 1, 2, 3 be the direction cosines of 3 mutually perpendicular lines. Find the…

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Q: 6. Find UV (dot a) Ū · V = (2, 3, -

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Q: 2. What is the angle between the vectors 7 = (-1,0,1) and w (0,1, 1)? 27n (A) 0 (B) (C) 4 (D) 5 (E)…

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Q: Find the Jacobian a(x, y, z) a(u, v, w) for the indicated change of variables. If x = f(u, v, w), y…

A: x=ρ sinφ cosθy=ρ sinφ sinθz=ρ cosφ

Q: 5. a) What is the orthogonal projection ŷ, of y = 1 (2) b) Compute the distance from y to the line…

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Q: 5. a) What is the orthogonal projection ŷ, of y = 1 = ( ² ) U = and the origin? -3 9 onto the line…

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Q: 4. For what value of h is vz in Span {v, v2} and for what value of h is {v1, V2, V3} linearly…

A: v1=1-32, v2=-39-6 and v3=5-7h

Q: Let a E R" be fixed. Suppose that vectors x, y E R" are related by the equation a = x+ (x.y)y. a)…

A: Solutions

Q: Given u = (-5,0) and v = (-8, 7), find the projection of u onto v. Round to two decimal places, if…

A: The given vectors are The objective is to find the projection of u onto v.

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: Which of the following is the closest point on the curve y = V X to the point (3,0)? °(들이) 5 2 'V 2…

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Q: -2 12. Calculate an orthogonal projection of u onto v if u = 2 ,v = 2 3

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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: 1: Let u = (-3,2, 4) and v = (2, -4,6). a) Find u o (v), b) Find u x v. c) Find Proj,u.

A: Here given that                        u=(-3, 2, 4)                and  v=(2, -4, 6)

Q: if u = <1,-3,1> and v = <2,2,2> then find the projection of u onto v

A: The objective of this question is to find the projection of vector u onto vector v. The projection…

Q: Q4 Evaluate S SR (x + 2y) dA where R is the triangle with the vertices (0, 3).(4, 1) and (2,6) using…

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Q: Let u = h = , V= -3 7 2 and w= For what value of h is w in the plane spanned by u and v?

A: The given vectors  and .The objective is to find the value of  for which  in the plane spanned by…

Q: Find the angle in degrees between u = (1, 2, 0) and v = (1, -2, 1)

A: Given, u=1,2,0v=1,-2,1 The formula for finding the angle between the two vector is, cosθ=u→·v→u→v→

Q: Determine whether u, v and w lie in the same plane when positioned so that their initial points…

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Q: shows the image of (D2 • Ry-axis)(4, -3)?

A: D2∘Ry-axis4,-3 this means 4,-3will be reflected over the y-axis. And then it will be dilated by 2.…

Q: (d) Passing through the point (0, 1, 2), perpendicular to the line L and intersects L. L(xo. v) =…

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Q: 47. Determine if AP is tangent to circle 0. A A. yes B. no 5 12 13

A: Given.

Q: Calculate the dot product of x = (3, -2, 0, 3) E R and y = (1, 2, 3, 4) ER4.

A: The dot product of two vectors x=(a1,a2,a3,a4)  and  y=(b1,b2,b3,b4)in 4th-dimensional space is: x.y…

Q: Let = -2- 4 V u = −2+ 4 Calculate , ul, (the angle between (2 decimal places) lull = + 5 K, and -…

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Q: Que. 1: Examine the following vectors for linear dependence X, =[1 2 4], X, = [2 -1 3], X, =[0 _1…

A: Write these vectors as rows in the matrix, convert the matrix to echelon form. If the echelon form…