Explain why the lines below are skew. l1: (x, y, z) = (-2, – 2, – 2) + n(1, 2, 3) and l2: (x, y, z) = (1, 1, 1) + r(1, – 3, 5)

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

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Q: T(x,y, z) = x² + 2y² + z

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Q: Find fx and fy, and evaluate at the given point.

A: The given function is: fx, y=xyx-y and the point is 2, -2. To find the fx and fy, first…

Q: F= [y°, 2², x²], C : r= [3cost, 3sint. 2t], 0 < t < 4n

A: Given that F=y2, z2, x2 and the curve, C, such that, r=3cost, 3sint, 2t for, 0≤t≤4π. Differentiating…

Q: If C is the z-axis from the origin to the point (0,0, 2), then So(3j – 3k) - d - dr |

A: If C is the z‐axis from the origin to the point 0, 0, 2, then ∫C 3j→-3k→.dr→=?

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

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

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Q: 10. In AXYZ shown below, medians XE, YF, and ZD intersect at c. F D Y E If CE = 5, YF = 21, and XZ =…

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Q: Q5) if z = 1./(3+x.^2+y.^2), where x and y = -3:0.1:3, could you plot x,y,z as shown below: 0.3 0.25…

A: Given: z=13+x2+y2where,x=-3,y=1.3   Now plot the given function.

Q: Find (a) ker(T) and (b) range(T).T: R4→R3, T(w, x, y, z) = (2w + 4x + 6y + 5z, −w − 2x + 2y, 8y +…

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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: 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

A: Given query is to find the the distance between two skew lines.

Q: Find the distance between the given skew lines: y = 4+ 21, y = 7, z = 8 – 7t x = 9+ 81, x = 8 – t, z…

A: Consider the skew lines x=9+8t,              y=4+2t,                   z=8-7tx=8-t,…

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: 17. For what value(s) of k, if any, will the lines *+1_y+2 3 k 7=(6,−1,0)+t(6,1−k,2) perpendicular?…

A: Product of DRs of two perpendicular lines is 0

Q: For what values of the constants k and c does the line x- 3 _ y-2 z+1 * = = 2 lie in the plane x - y…

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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: 45. In AXYZ, W is between Y and Z. The coordinates are X(2,3), Y(5,0), Z(0,0) and W (2,0). What is…

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Q: Find the point of intersection of the lines r(t) = (1, 0, 0) + t(-7, 3, 0) and s(t) = (0, 1, 1) +…

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Q: Find the distance between the skew lines: x = 4+ 9t, x = 4 – t, y = 3+ 2t, z = 7 – 4t y = 9, z = 8+…

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Q: 4. Determine whether the pair lines are equal, parallel but not equal, skew, or intersecting. L1:x =…

A: Given:      L1:  x=1-4s, y=3+s ,z=8-6s      L2: x=2+3t ,y=2t ,z=-1-3t   For Parallel test:…

Q: Consider the skew lines: rị(s) = (s+1, –2s+2, –s+3) r2(t) = (-t, 2t, 3t +2) Find the distance…

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Q: dw dw Find ду and ду at the point (w, x, y, z) = (9,3,1,1) if w = x²y? + yz- z³ and x2+y² +z² = 11.

A: The solution of the problem is given in the next steps.

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: 4 - If w = x + 2y + z? , y = r2 + In(s), and z = 2r = X find at the point (r, s) = (-8,4). %3D

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Q: Find the distance between the skew lines: x = 8+6t, y = 5+ 9t, z = 7 – 5t y = 9, I = 6 – t, z = 2+…

A: Given, x=8+6t, y=5+9t, z=7-5tx=6-t, y=9, z=2+4t To find: Distance between the two given skew lines

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: 4. Determine whether the pair lines are equal, parallel but not equal, skew, or intersecting. Lị:x =…

A: Recall: Given two lines  L1:  x1=a1+b1s  , y1=c1+d1s   , z1= e1+f1s  L2:  x2= a2+b2t  , y2=c2+d2t…

Q: dw Find and using the chain rule. ди 3 w(x, y, z) = x = u² + v², y = u² + v², z = 2uv. %3D x² + y? +…

A: The solution is given as

Q: The equations [2, 1, 6] + t[6, 1, 4] and [4, 1, 3] + s[2, 10, 9] Are parallel Intersect at one point…

A: Topic = Lines Given lines are skew lines.

Q: We are given w = 2yln(y+2z)x2, where x=b√c, y=c-a2, and z=ab+1. Find the following ∂w/∂a at the…

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Q: g(x, y, z)

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Q: For the given data (0, 1), (1, 1), (2, 3), (3, 5) find the line y = ao + a1x that best fits the data…

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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: Y Find S Zdz Such that c is the line which joining A,B,C and D as follows A (o,1) yB (2,1) , C…

A: Here, firstly we have draw the line C with the given points. Then we have to find integration value…

Q: Find the distance between the skew lines i(t) = (3, 0, – 2)t + (7, 9, 0) and p(s) = (4, – 4, – 5)s +…

A: We have to find the distance between skew lines.

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 Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

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Q: {(x, y), 4.x2 + 9y² < 36} C R2 ected? pathwise connected? Justif

A: Connected and path connectedness

Q: Find the distance between the skew lines r(t)=⟨3,−2,−4⟩t+⟨−4,−2,5⟩ and p(s)=⟨5,2,1⟩s+⟨−6,4,7⟩

A: Given r(t)=⟨3,−2,−4⟩t+⟨−4,−2,5⟩ and p(s)=⟨5,2,1⟩s+⟨−6,4,7⟩

Q: o Find the Vf at the given point 2. (x,y.2)=(x² + y² + ²)² +In.xyz,P(-1,2,–2)

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Q: B is the midpoint of line segment AC. Find x C 5X-6 3X +4 Ox = -5 O x 2 Ox = 5 Ox = 10

A: A line segment is a finite section of a straight line. A mid-point of a line segment is a point…

Q: Find the values of ∂z/∂x and ∂z/∂y at the points z3 - xy + yz + y3 - 2 = 0, (1, 1, 1)

A: Given: z3-xy+yz+y3-2=0  At the points (1,1,1) To find: The values  of ∂z∂x and ∂z∂y.

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: We are given w = 2yln(y+2z)+x2, where x=b√c, y=c-a2, and z=ab+1. Find the following ∂w/∂a at the…

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Q: Tind The E94ation of line which is normal to the lines X-2 = マー 3-2 %3D - and 2-X %3D 2. 3. 2.

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Q: 5. Find fx, fy, and fz given x®y? f(x, у, 2) z4 %3D

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