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

Q: ?w Əv у Find when u = 0, v=0 if w=x² + ₁ x=6u-2v + 1₁ y=u+4v - 1.

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Q: OLet U=(2,-37, V=Fl,5), W=(4,-62 Find U•V

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Q: Find f.(x, y) and f,(x, y) for f(x, y) 3x3 + 8y? – 6x + 4y and evaluate each at f(4, 5). f.(x, y) =…

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Q: Given u = (-2, 4) and = (1, 6), find 3(uw).

A: The vectors are given by u→ = -2, 4w→ = 1, 6 To evaluate: The value of 3u→·w→

Q: Find Duf at P. f(x, y, z) = 6x³y³z³; P(2, — 2, 2); u = Duf = i + - 2|3 k

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Q: Solve for w where u = (1, 1, 0, -1) and v (0, 3, -1, 2). w + 4v = -3u %3D

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Q: Find ∂w/∂v, if w = 3x4-5y3+z5-10, x = 3u-4v, y=5u+2v, z = u+8v. Write in terms of the two…

A: Chain rule of derivatives

Q: Calculate the length of PQ where P = (-2,1,6) and Q = (-3,4, –1).

A: We will find the length of PQ→ in the following step

Q: Find an expression for the exact angle 0 between u and v when = (4,7) and v = (-5, 8). (3, –1, 1)…

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Q: uppose ū = (1, −3,−1) and v = (1, -5, -5). Then:

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Q: Determine Duf(-1,3, 2) for f (x, y, z) = e2ay° + 4x²yz in the direction (3, -2, 5). V =

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Q: Given vectorsu = (1,3) and v (0. -3), find u

A: Given vectors are The vector u.v is evaluated as follows

Q: Find u v. = (9, 2) v 3 (-8, 4) V: U V D

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Q: A 4,-1) B(4,-2) find lime x approachesto1 from postve dinection.

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Q: Let L, be the line passing through the point P-(1, -7, 5) with direction vector d-[1,-2, 0], and let…

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Q: Perform the indicated operations for the given vectors. r=(4, 7), -(10, -10)..-(1, -6) Find v+s-r…

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Q: a. A nonzero vector perpendicular to both [-1. 3, 4] and [-2. -1, 3].  b. The distance from (2, -1,…

A: Let's go through each of the questions:a. To find a nonzero vector perpendicular to both [−1,3,4]…