Find the distance of the point (2, 2, –5) from the line r(t) = (1+4t, –1+ 4t,7 – 3t) %3D swer:

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

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Q: The two planes r+y +z= 1 and r – 2y + 3z = 1 intersect in a line l.

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Q: Qz find the alistance from the Point to the line (zy-) , メーマty4zt?2t

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Q: Find the length of the curve. r(t) 4t, t2, ostsi

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Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: H

Q: Find the length of the curve. r(t) = 3ti + 8t3/2j+ 12t2 k, 0 sts 1

A: The given curve is: r(t)=3t i+8t32 j+12t2 k ;                0≤t≤1

Q: Points X and Y are respectively 12 m north and 5 m east of point Z. Calculate XY.

A: To solve this problem we use the Pythagorean theorem

Q: Use Eq. (5) to find the point P nearest to Q = (2, 1, 2) on the plane x+y+z=l.

A: Consider the provided information, Find the point P. The normal vector to the plane is 1,1,1. And…

Q: Find the length of the curve. r(t) = ( 8t, t², ), 0 <t< 1 %3D 12

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Q: utwards from the point (0 nd S, the top half of the

A: Given, the vector field                        E(x, y, z)=x, y, z-3this vector field can be…

Q: ) Find an equetionof tue tenyent line to the greph of d= In(x') at the point (l,0). Angwery8 a) y*-5…

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Q: the distance between the two skew lines L and L2. L: x=3+3t, y=-1-4t, z=4+2t. L2: x=6+5p, y=3-p,…

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Q: Find the length of the curve 4t2 -1 dt, y = %3D 1<x<3 8. 15 104 3 3.

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Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Find the exact length of the curve. x = et – t, y = 4et/2, 0st < 5

A: Find the length of curve:

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

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Q: Q8) The distance between the line x=-1+t, y=3+2t, z=-t and the plane :2x-2y-2z=3 is

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Q: Find the length of the curve. r(t) = 4t, t2, t3,     0 ≤ t ≤ 1

A: To find the length of the given parametric curve

Q: عنوان الدرس. / الموافق Find equation of the plane that cont the line s L,:X= Sty=Ct 6+2t .....…

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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: Find the point (x,y) of x^2+14xy+49y^2 = 100 that is closest to the origin and lies in the first…

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Q: Find the point (x, y) of x² + 14xy+49y = 100 that is closest to the origin and lies in the first…

A: we draw a shortest straight line from origin to line, which will we perpendicular then we will find…

Q: Find the length of the curve. r(t) = (4t, 0 <ts 1

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Q: Find the length of the curve. r(t) 4t, t², Osts1

A: To find arc length of curve

Q: Find the length of the curve. r(t) = 4ti + 8t3/2j + 9t2 k, 0st<1 %3D

A: Please see the answer below

Q: Evaluate yz dx +y dy +a dz, where C is the line segment from (2,0, –1) to (4, 1, 2).

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Q: Compute Δy and dy for the given values of x and Sketch a diagram showing the line segments with…

A: Given: Now,

Q: Evaluate ∫C x ds, where C is the parabolic curve x = t, y = t2, from (0, 0) to (2, 4).

A: Given: Parabolic curve x=t, y=t2 from (0,0) to (2,4)

Q: Find the length of the curve r(t) = (1,t2, t³). 0<t < 1.

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Q: Find the length of the curve y = V- from z =1 to r = e. 3

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Q: Find the length of the curve. r(t) = 8i + t2j + t³ k, 0sts 1

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Q: Find the length of the curve. 6t, , r(t) 0 <t< 1

A: Given:-r(t)=6t, t2, 19t3,         0≤t≤1since we have to find the length of curve.

Q: Find the point at which the line F (t) = +t intersects the yz plane.

A: Given: An equation of a line in the parametric form is, r→t=&lt;2,-7,7&gt;+t&lt;-5,-6,6&gt; The…

Q: (b) Find the points on the line r(t) = (t, 1+2t, 1-2t) whose distance from the plane 2x - 2y+z=1 is…

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Q: O Find All the ASymploles of the Cerve 3x3 +22y-7ay²+2y"-14x4+7y²+4x+5 =0-

A: Total Asymptods are 3 .

Q: Find the tangent plane to the equation z = 3x2 + 4y? – y at the point (3,5,68)

A: We have to find the tangent plane equation to the given surface at a given point.

Q: Find the length of the curve r(t) (1,t²,), 0sts1 %3D «3 Ost<1

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Q: Evaluate f.y ds where C is the upper half of circle x? +y² = 9, traversed in the counterclockwise…

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Q: Ex (50) / Find the distance from the line = 2 +t, y = 1 +t, z = -1- 2t to the plane x + 2y + 6z = 10

A: Using. Distance formula form line to plane,

Q: Find the length of the indicated portion of the trajectory. r(t) = (1+2t)i + (1+8t)j + (4 – 4t)k, –…

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Q: Find the length of the indicated portion of the trajectory. r(t) = (1 + 3t)i + (1 + 5t)j + (4 –…

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Q: Find the length of the curve traced by r(t) = t^2 i + (((t^3)/3) + 2)j, for 0 ≤ t ≤ 1

A: The solution is given as

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

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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: Find the isogonal trajectories to a family of straight lines y= cx that cut the lines of the given…

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Q: Find the length of the curve. r(t) 4 it2j3k, 0 st s 1

A: Consider the curve x = 4, y = t2 and z = t3.The derivatives are

Q: Find the tangent plane to the equation z = 5a° + æy? + 2 at the point (2, – 4, - 6)

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Q: х2, у3D 12 — х, х 3D 0, around line y — -2

A: the function given to us is y = x2 and the line about which it revolves is y = -2 we have to use the…