14. Find the distance between the two skew lines. x = 2+t x = 4+s y = 3-t y=1+s z = 4t z = 2- 2s

Q: Find the length s of the path (3 + 10r,9 + 2r312) over the interval 5 < t < 6.

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Q: Find the distance between the following skew lines -y+14, z= X-1 y =z+3 2 2

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Q: T(x,y, z) = x² + 2y² + z

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Q: Find the equations of the normal line to the surface z = 8x°y" at the point (– 2, – 1,64). y = z = -…

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Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x=1+2t, y=5+15t, z=-2+6t, then…

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Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x = 1+2t, y=5+15t, z=-2+6t,…

A: given : the equations of two skew lines are: L1: x=1+t, y=1+6t, z=2tL2: x=1+2t, y=5+15t, z=-2+6t D…

Q: 20. Evaluate l Vx + 2y ds, where C is a. the straight-line segment x = t, y = 4t, from (0, 0) to (1,…

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Q: 13- Find the length of the curve a) r(t) = 4costi + 4sintj³ + 3tk³ 0< t < 3n b) r(t) = 4ti + 4tj¬ +…

A: Please refer the image,

Q: 3. If V =(3x'y-z,xz' + y",-2r?:'). Find grad div at the points (2,-1,0).

A: Given , V=&lt; 3x2y-z, xz3+y4, -2x3z2 &gt; To Find , grad divV  Let  V=&lt; V1 ,V2 ,V3 &gt; On…

Q: Which of the following represents the distance between (X. (X2. Y2) O A. d = 2 / (x2 +1) + (y2 +Y1)…

A: Given two points, A(x1,y1) B(x2,y2) distance d=?

Q: are two points find d.c's of OP, QO and PQ where O If p(2, 3, 6), Q(3,4, 5) is the origin.

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Q: Find Duf at P. 2 + 2. 5,3 4 f(x, y, z) = 6x³y°z*; P(1, – 2, 1); u = Duf i

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Q: If D is the distance between the skew lines L1 x=1+1, y=1+61, z=21 L2 x=1+2t, y=5+151, z= -2+61.…

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Q: Evaluate the line integral ∫_c (2x − y) dx − (x+ 3y) dy , where C is a straight line from (1,1) to…

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Q: Show that if x', y are the deviation of the variables from their means, then x Yi r=1. Σ 2N - Ox Oy…

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Q: If a particle moves on a line according to the law s = t§ + 2t³, then the number of times it…

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Q: 15. In AXYZ, XY YZ and m/XYZ = 46*. %3D 46

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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: Find the distance between the skew lines defined by L1: ri(t) = L2:r5 (s) =

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Q: 4. Evaluate S. (z – 4) dz, where r is a contour from the two line segments, the first from z = -3 to…

A: Contour integrals or line integrals along a path C   can be written as ∫Cf(z) dz=∫abf(z(t) z'(t) dt…

Q: 4. ( , Give a case in which |(x, y) x||yll. 5. Let X e PQ. Show that if X (1-t)P+Q, where t> 1, then…

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Q: 20. Evaluate J Vx + 2y ds, where C is a. the straight-line segment x = t, y = 4t, from (0, 0) to (1,…

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Q: ize P= 3z + 4y E to 21 + vS 16 27+ 3y S 24 z20, v 20

A: Introduction: Linear programming is the most basic method for optimizing a problem. We can use this…

Q: Find the distance between the following skew lines -y+48, ,z=0

A: The given equation of skew lines- x2=y+48,z=0x-12=y2=z+3 Above equations can also be written as-…

Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x=1+2t, y=5+15t, z=-2+6t, then…

A: here we the formulae   the a plane have normal n→=&lt;a,b,c&gt; and passes through a point (x1 ,y1…

Q: (a) Compute S ædx + ydy + (x + y – 1)dz where C'is the line segment from (1, 1, 1) to (2, 3, 4).

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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: The distance between the following two skew lines is Line#1: [x, y, z] = [1,1, 10] + t[5, –3,0]…

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Q: If D is the distance between the skew lines 4 x=1+t, y=1+6t, z=2t L2 x=1+2t, y=5+15t, z=-2+6t, then…

A: first we will  convert given parametric equations of lines, then we will find  a1,b1,a2,b2 after…

Q: If D is the distance between the skew lines L: x=1+t, y=1+6t, z 2t L2: x=1+2t, y=5+15t, z= -2+6t,…

A: Two lines in space can be skew, parallel and intersecting. Lines are skew if they are neither…

Q: Find the distance between the given skew lines: x = 4+9t, y = 5+ 3t, z = 7- 6t x= 8 – t, y = 9, z =…

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Q: EVawate Fy (Y,y) q Jylx,y) at the indicated point. fir.y)= In (ry) at (-2,-3)

A: Given query is to find the derivative at indicated point.

Q: et y = [ 2   3   -1] and u = [ 2   -6   -6] compute the distance d from y to the line through u and…

A: first we shall find equation of line then find distance from line of that point

Q: 4. The Cov(xr, y,) between x and y for the following data : Σ-15 Σy= 36, Σxy 110, X; 7 = 5 is :

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Q: 2. Evaluate (3xy+iy²)dz along the straight line joining z = i and z = 2 – i.

A: Given the Integral, ∫i2-i(3xy+iy2)dz We, know that z=x+iy ⇒dz=dx+idy, When z=i    ⇒x=0 and y=1  When…

Q: If D is the distance between the skew lines L: x=1+t, y=1+6t, z=2t L2 x=1+2t, y=5+15t, z= -2+6f,…

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Q: Find the distance between the skew lines: x = 5 + 8t, y = 1+ 6t, х— 2 — t, z = 4 – 9t z = 4+ 8t y =…

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Q: 2² dædydzB = {(æ, y, z) =E R° 0 < æ < 1,0 < y < 1,0 < : < x}

A: Given triple integral  ∭Bx2dxdydz, where B=x,y,z∈R3:0≤x≤1,0≤y≤1,0≤z≤x. We have to evaluate…

Q: | 6. Let y = 3 and u = . Compute the distance from y to the line through u 1 2 and the origin.

A: Given: y=-231  and u=1-12 To compute: the distance from y to the line through u and the origin.…

Q: Find the distance between the skew lines: I = 9+9t, y = 2+5t, z = 3-7t x=6-t, y = 9, z = 6+6t NOTE:…

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Q: (b) ƒ(x, y) = Vy – x · In (y+x) -

A: Given (b) f(x,y)=y-x ln (y+x)

Q: Find the distance between the skew lines defined by L1:(t) = L2: r2(s) =

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Q: The area bounded by the curve y = 6z and the lines a = 5 and z= 8 above the T aris is 234.00 square…

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Q: 11.) If mVQ = (y + 7)', mQR = (x + 11)', mRS = (3y)', and mST = 65', find the values of x and y. %D…

A: Given- If mPQ⏞=y+7°, mQR⏞=x+11°, mRS⏞=3y°, mST⏞=65° To Find- The value of x and y.

Q: Find the distance between the skew lines: y = 1+3t, y = 9, x = 3 + 8t, z = 4 – 9t x = 5 – t, z = 4+…

A: Given equation of line L1: 3+8t   , y=1+3t   , z=4-9t L2:   x=5-t  , y=9   , z=4+8t

Q: xlet X,Y,7 be v.V.J with Joint fA くれく くらくtyerzc

A: The joint probability density function is given to us the conditions on x, y, z are also given to…

Q: Find the distance between the skew lines: x = 5+ 6t, y = 2+ 3t, z = 8 – 3t z = 1+ 2t x = 9 – t, y =…

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Q: 4 - If w = x+ 2y + z? , x= , y =r2 + In(s) , and y = r2 + In(s) , and z = 2r aw find at the point…

A: Using chain rule the given question has been solved in step 2.

Q: 3. If V =(3r°y-z,x²+y",-2r:'). Find grad div, at the points (2,-1,0).

A: