Let S be the surface of the box [0, 1] × [0, 2] × [0, 4], and let F = ryzi+zyzj+zyzk. Find the flux of F across S. Select one: a. 28 O b. 31 C. 19 O d. 25 O e. 22

Q: Determine the value of k for which the vectors u and v are orhogonal u = (1, k, –3), v = (2k, –5, 6+…

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Q: = Complete the following truth table. Use T for true and F for false. You may add more columns, but…

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Q: Let a = (0, 2) and b = (- 5, 1). %3D %3D | Find the angle between the vector, in degrees.

A: Given vectors are: a→=0, 2 and b→=-5, 1

Q: Calculate v x w: v = (3,8, 8), w = (1,1,4) V X w =

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Q: -3 3 Let u = -5 and i: 7 Find a vector w not in span {u, v}. 4 -3

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Q: 3. [32] −1 4-3 4. 5. [. |_3 -4 2 1 2 -1 4,

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Q: Let = [-3 1] and = [1 2]. Find the following vectors. [ ]]. ]]. u = 7y= = [1 w = 2x + 7y = [ v=27=…

A: Given: Let x→=[-3  1] and y→=[1  2].

Q: Find the value of β for which w =〈−2, β〉 is parallel to v =〈4, −3〉.

A: Two vectors are parallel if the angle between them is 0 or π. That is, the vectors are pointing in…

Q: Let u =(0,1,2) and v=(-2,2,0). Find %3D a. A vector w orthogonal to both u and v. b. The area of the…

A: The orthogonal vector both u and v is u×v . And the area of parallelogram is |u×v|

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: Let P = (3, –2), Q = (1,4), R= (-2,5), S= (-4,6) Find the component and linear %3D combination form…

A: We have to find vectors

Q: 4.18. Given vectors u = 3j – - 6k and v = 6i – 4j – 2k, find the dot product of u and v.

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Q: Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

A: Calculation:Since it is given that v and w are orthogonal, v ∙ w = 0.

Q: let v =〈−2, 5〉and w =〈3, −2〉. Sketch v, w, and 2v − 3w.

A: Given vector:                   v=-2,5 and  w=3,-2   Algebra of vectors: Let v = x1, y1 and w =  x2,…

Q: Consider the following. u = (-5, 5, 4) v = (0, 1, 6) Find u x v.

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Q: Let L₁ be the line passing through the points Q₁-(-1, -3, 1) and Q₂=(-4, -6, 2). Find a value of k…

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Q: Let u = (2, -1,3), v = (3,0,1) and w = (-1,-1,3). find all values of I, m and n such that lu + mv +…

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Q: Let U₁= - 3. For what value of h is j in the plane spanned by ₁ and ₂? h V₂ = -9 [18] ý 11 -

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Q: Let u= 31-2j + k and v= 2i – 2j + 2k. Find ux y.

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Q: 3. Find all real numbers t for V = (20 t,4t - 4,5t², t²) are orthogonal. - which = (1,5t,-4t, t³)…

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Q: Q5.Find a vector parallel to the line of the intersection of the planes 2x + y – 2z = 5 and. N, = 2î…

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Q: 2. Let A = {2, 3, 5} and B = {x, y}. Let p1 and p2 be the projections of A × B onto the first and…

A: a. Find p1 (2, y) and p1(5, x). What is the range of p1? To find p1​(2,y) and p1​(5,x), we use the…

Q: Let u=i+j, v=j and w=k. Find c₁, c₂ and c3 such that 5i +5j + 4k =q₁u+c₂v+C₂W.

A: Given: u=i+j  v=j  w=k

Q: Q5.Find a vector parallel to the line of the intersection of the planes 2x + y – 2z = 5 and. %3D N =…

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