GD = 三|=▼ 冊 4 5 6. 1. ASTU with S(1, 2), T(4, 3), and U(5, -3); translate left 4 and up 3. 2. Parallelogram ABCD with A(-4, -3), B(-1, 4), C(5, 6) and D(2, -1); translate according to the rule (x,y) → (x+2, y-4). 3. Rectangle PQRS with P(4, 0), Q(3, -3), R(-3, -1) and S(-2, 2); translate <-2, 1>. =-1

Q: f(æ, y, z) = æ²y+ 2y²z+ 3æz?. Compute fa: (1, 1, 1). None of these. 3

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Q: Find symmetric equations for the line through (1, 3, -2) and perpendicular to both u and v, where u…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Determine D„f(4, –1,6) for f(x,y,z) = ex³y + 4zx³ in the direction of (–3,2,6). %3D

A: Given that fx,y,z=ex2y+4zx3 Then  ∇f=∂∂xi+∂∂yj+∂∂zkex2y+4zx3=2xyex2y+12zx2i+x2ex2yj+4x3k

Q: 5) s how that the line af intersection f the Planes X+24-22= 5 and 5x-2y-73D0 is Parallel to theline…

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Q: А Q(1, 1) в Q(2, 0) vyQ(1, y) 3xQ(x, 2)

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Q: 24 dA - I 3x – Y when D is the parallelogram bounded by x – 2y = 0, x – 2y = 2, - and Зх — у 3D 1,…

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Q: Find the average value of f(x, y) over the plane region R.

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Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

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Q: Find (au / ay) at the point (u,v) = (√6, − 1), if x = u² + v² and y= uv. ди (2) (Simplify your…

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Q: 8. The distance between the planes 2r-y-2z 5 and 2r – y - 2z = 7 is A C 2 9 dn 24

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Q: At what point does the line: L: x=-1, y= 10 + 31, z= 4 +3t im plane 1:x- 2y + 5z + 16 = 0?

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Q: The line that passes through the points (2,0), (0,1) is x+2y = c, where c = 1. O True False

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Q: 4. If A = 3xyz²i + 2xy³j- x²yzk and p = 3x² - yz, find (a) V-A, (b) A-V4, (c) V-(Vo) at point (1,-1,…

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Q: For planes 2x + y – z = 2 and 2x + 3y + 5z = 4,

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Q: T: R2 R2 is defined by х + 7х, [3x, – 4x2] X1 %3D and B = {u,,u,} and B' = {v,v,}, where %3D -- --…

A: Given transformation T:R2→R2, defined by Tx1x2=x1+7x23x1-4x2 and B=u1, u2 and B'=v1,v2 Here u1=22,…

Q: dw dw Find ду at the point (w, x, y, z) = (- 4,1, - 1,1) if w = 4x y + 4yz - 4z° and x? + y? + z² =…

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Q: 2 W = Span- - 1 1 .Then, the distance and y = 1 -3 -21 3 11 ny to W is

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Q: Sc 7ydx + 3z dy where C is the straight line path from (2, 4) to (4, 7).

A: The parametric equation of the straight line between the points (a,b), (c,d) is x-ac-a=y-bd-b=t,…

Q: If A = 3xyz²i + 2xy³j-x²yzk and p = 3x² - yz, find (a) V-A, (b) A-Vq, (c) V.(Vo) at point (1,-1, 1).

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Q: 1. The lines 4: x=1-t, y=2+t, z=-2-t; 12:x=3+s, y=-1+s, z = 2s are skew.

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Q: Separate ỷ into y and y if y is in the direction of u %3D

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Q: 22. The line 3. is parallel to the line 2. x+3 A. 3 y+1 z-1 %3D 3 B. f = î - i+ 5k + t(3î + 3j + 2k)…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 11. Determine whether the lines L₁ given by x=t, y = 1+ 2t, z = 2 + 3t, (with x < t < oo) and L₂…

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Q: The equation of the line segment from A(3, – 4,4) to B(5,2,5), 0<t<1 is a. r= (3+ 2t)i +(- 4+6t)j+(4…

A: Topic = vector  correct option 'a'

Q: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

A: Determine the way in which the line [x, y, z] = [5, −9, 3] + k[1, −12, 2] intersects the plane [x,…

Q: ) s how that the line af intersection f the Planes X+2y-22%= 5 and 5x-2y-Z=0 is Paraliel to theline…

A: Solution is written in below steps.

Q: Find b∈R so that ∫C4x^2dy − 2xydx = 53, where C is the segment from (1, −5) to (−2, −3), followed…

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Q: d. The plane through P,(2,4,5) perpendicular to the line x=5+t y=1+3t .

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Q: 1. Evaluate 4x³ds, where C ie the line segment trom -2,-1,QL,4). らt Xz xlt)= (1-t)(-2) + t(1) E) :…

A: Introduction: A line integral is an integral that determines the function to be integrated along a…

Q: * Let LIEX-54+10=D0 L2=4X+y-1-O be two lines. 1 Show that the lines L and Lz are not parallel.

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Q: )find the dis tance between the Linel L) through A(1, 0,-1), B (-1,,0) andthe Line (L2) th rough C…

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Q: If A = 2.x2i – 3yzj+xz²k and o = 2z – x°y, find A.Vø at the point (1, –1, 1). |

A: The gradient is calculated using the del operator and it can be represented as ∇=∂∂xi^+∂∂yj^+∂∂zk^.…

Q: Determine D,f (4,-1,6) for f(x,y,z) = ery + 4zx in the direction of (-3,2,6).

A: Given fx,y,z=ex2y+4zx3 in the direction of -3,2,6

Q: The equation of a line perpendicular to 4x+7y– 63 =0 is Oy- z 6 Oy--- I. Oy =z+

A: See the details solution in below

Q: 4) Lett =,u = x? - y² ,v = 4xy³. Find %3D ax ду

A: t=uv

Q: The equation of the line segment from N(3, – 4,5) to M(5,2,4), 0sts1 is a. r= (3 + 2t)i +(-…

A: Equation of line segment

Q: 5) s how that the line af intersection f the Planes and 5x-2y-Z=0 is Paraliel toG Pheline X+23-22= 5…

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Q: 26 + 4z4 – 2z2 +1 dz (z – 2i)6

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Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

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Q: Suppose T(x,y) = (2x, 2y) and U(x,y) = (x, -y). Is T∘U=U∘T?  Justify your answer.

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Q: dw and at the point (w, x, y, z) = (22,1, – 1, – 2) if w =2x²y? +2yz- 2z° andx? +y² +z? = 6. Find…

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Q: Find Sc((x² + 3y)i + 3y³j) · dr' where C consists of the three line segments from (2, 0, 0) to (2,…

A: Given ∫x2+3yi→+3y3j→.dr→ where C consists of the three segments from (2,0,0) to (2,2,0) to (0,2,0)…

Q: Ye = C1 + C2x + Cze3x + C4xe3x Yp = Ax² + Bx + c Since Czx & Bx and C, & C are similar how do I use…

A: Complementary solution is: yc=C1+C2x+C3e3x+C4xe3xParticular solution is:yp=Ax2+Bx+C

Q: 2x + 3y Find -dA, where R is the parallelogram enclosed by the lines 4x – 4y -- 2x + 3y = 0, 2x + 3y…

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Q: , in general form (x + y2 + Bx + Cy + D = 0), centered a he lines 2x + y + 10 = 0 and x - 2y - 5 = 0…

A: We have to find the equation of a circle whose center is the point of intersection of,  2x+y+10=0…

Q: Find the z-coordinate of the foot of the perpendicular from A(1, 1, 1) on the line joining B(1, 4,…

A: We will solve the problem.

Q: If u=2x+y and v=x-2y then the st ream line is y2 x2 2ху+ 2 صواب ihi

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Q,3 Evaluate [II, xyz dxdydz, 3 < x S-2,0 < y S 1,0 S zs-

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Q: 16. Find the points of intersection of x' = 4y and y= 4x. (as:(0,0,(16,64)

A: My Dear student according to the rules of Bartleby we can solve only one question post others as a…