Let u = (5,-5, -7) and 7 = (-6, 1, 2). Compute the following: úxv= v X ū= úxu 3 (u xv) = ū × (30) = (u + v) × v = |

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: Find mZVUZ if mZZUT= 16x + 2, | MLVUZ = 24x – 1, and mZVUT = 16

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Q: Differentiate. x3 7) y = X- 1

A: Given : y = x3x-1

Q: F .2 .2 x- +y at A=(2, 3), B=(-2, 2) and C=(3, -4).

A: 1.) div F at A(2,3) = <4,6>2.) div F at B(-2,2) = <-4,4>3.) div F at C(3,-4) =…

Q: Find div(V), where V= (x²+y² + z²)¯²(-3x, -3y, –3z].

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Q: Find the Cross product of A= and B=

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Q: Find the cross product x where = 71-7j -4k and 7 = (-4,-3, 4). úxv=

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Q: Find the cross product a × b where a = (0, 3, 4) and b = (5,1,2). axb =

A: Step 1: Step 2: Step 3: Step 4:

Q: Let u = , v = , and w = . find uw

A:

Q: If f(x) ' (1 ) cos (x)

A: We have f(x)=xcosx. So,            f'(x)=xcosx'            =xsecx'            =x'secx+secx' x…

Q: Let F = (, , 2). Calculate div (F) and curl (F). (Use symbolic notation and fractions where needed.)…

A: We have to calculate  and .

Q: Let A = (-0,0), B=(0,0) then AUB=

A:

Q: (2x) (3y+8) (2x+4) R 5. mZQ = mZO =

A:

Q: Graph the two vectors x= (5, 1,3) and y=(-1,3,1

A: Topic:- 3D

Q: Express the following as a linear combination of u = (6, 1, 7), v = (1, -1, 4) and w = (1, 8, 7).…

A:

Q: Suppose [V] B₁ [V] B₂ = 7 1 3 -[-]-* *, - {{; } [³])} and B₂ - {[²][³])}; [ 2 ] = find B₂ = If B₁ =…

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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: Express x XOR y with only AND, OR and NOT.

A: We can write-                    x OR y = NOT (  NOT x   AND   NOT y )

Q: the smallest possibl product of the two numbers x>= 0 and y<= 0, such that 2x-y=120 is:

A: Let x and y be two numbers such that  x≥0,y≤0, 2x-y=120y=2x-120

Q: For what value of x, 3x 2х 2:

A:

Q: If (2,9)=, then f„- If f(x,y)

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Q: If web₁x-b₂y-b3z, w= where b₁,b2, b3 are constants and b² + b² + b = 1. Show that 8² w 8² w 8² w əx²…

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Q: The height of 10 plants is measured in inches and found to be 12,6,15,3,12,621,15,18 and 12. Verify…

A: We know that, Mean, X bar = (summation Xi)/m Here n= 10 X bar = (12+6+15+3+12+6+21+15+18+12)/10 = 12

Q: Is the ordered pair (4, 7) a solution to which equation O 3x + 4y = 4 O 3x = -4y+ 4 O y = 3/4x + 4…

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Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

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Q: Sketch v = (−2, 1), w = (2, 2), v + 2w, v − 2w.

A: Given vector, v = (−2, 1), w = (2, 2)

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: Evaluate (521 + 3z2)

A:

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

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Q: Prove that if x+y=%30 then y=-x

A: See the attachment

Q: Vxdx 2. For J T-Vx use 4 O u = JA u = x O u = Ja

A:

Q: a2z If z = In(x² + y²), find a²z + dx2 ду?

A: Given, z=lnx2+y2