25. Determine the distance between the parallel line {y = 5-t, te R and the plane {y = 2-s -t, s,t E R. Z = -4 |z = 1 + 5 -t

Q: 25. Find the intersection of the line [x, y, z] 2х — 4у + 7z —26 %3D 0. [1,4, – 2] + t[1, – 1,3] and…

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Q: find the plane containing the intersecting lines.  L1: x = t, y = 3 - 3t, z = -2 - t; -inf < t…

A: This question is taken from the planes in which we have to find the plane equation. We can write the…

Q: Evaluate the line itegral where C is the upper half of the circle z +y = 3.

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Q: Calculate the distance from the point (4,−2,7) to the plane x−3y+5z=−8.

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Q: 1. Using Euler's equation, show that the shortest distance between two points (r1, yn, z1) and (r2,…

A: Given, the points are (x1, y1, z1)   and  (x2, y2, z2).

Q: A________ is the set of points P in the plane such that the ratio of the distance from a fixed point…

A: The conic section is known as the set of points, in which the curve of any of the conic, that are,…

Q: Evaluate x ds, where C is a. the straight line segment x =t, y =. from (0,0) to (6,2) b. the…

A: We need to evaluate ∫Cx ds

Q: 4z: Given two lines (z++l, 5t-5,lot )f ( 34, zt+3, zt+1) located in Sicde plane, fine th plane ?

A: Equation of the plane passing through to lines can be calculated as below,

Q: Calculate the distance from point s(10, -8, 10) to the plane 2x + 2y + z = 4 O 10 O 10 의 ~m 의 29

A: Given query is to find the distance between the plane and point. The given point is S(10, -8, 10)…

Q: Determine whether the line L : x = 3 – 4t, y= 5+2t, z = 5 + 4t, - is parallel to the plane x - y +…

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Q: O Find all values of t such dhat dhe dangent line a CI()=<E,tit3-37 is parallel to xy-plane.

A: Given:-r→(t)=&lt;t, t, t3-3&gt; and the tangent line parallel to XY-plane (z=0)now,tangent vector on…

Q: 1. Find the distance from the point S(2,-3,4) to the plane x+2y+ 2z =13

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

Q: Determine whether the plane x + y + z = 9 and the line x = t, y = t + 1, z = t + 2 are parallel,…

A: Given: The planes x + y + z = 9 and the line x = t, y = t + 1 , z = t + 2.   To determine Whether…

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

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Q: 1. Determine whether the lines L₁ given by z=t, y=1 with -∞ <t<∞o) and L₂ given by z=2+s, y = 3-2…

A: Introduction: If two lines are parallel then the ratio equality is true between them. And if two…

Q: Find the distance from the point (1, 2, 0) to the line æ = 3t, y= 1, z= 2 – t.

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Q: When is An angle in the xy-plane is said to be in standard position?

A: An angle is in standard position if its vertex is located at the origin and one ray is on the…

Q: The distance from (4,-5, 10) to yZ-plane is O A.4 O B. 5 C. /141 OD.10 OE. 125

A: Solution is given below:

Q: Find the distance between the parallel planes. x + y + z = 1 and x + y + z = 3

A: The distance between two parallel planes is the shortest distance between their surfaces. Distance…

Q: Find the distance from the point (−5,2,−3) to the (a) xy-plane (b) xz-plane (c) yz-plane (d) x-axis…

A: We know that distanced of xy-plane from the pointx0,y0,z0 is given by d=z0…

Q: Use Eq. (8) to find the distance from Q = (1, 1, 1) to the plane2x + y + 5z = 2.

A: Find the distance from Q=(1, 1, 1) to the plane 2x+y+5z=2 or 2x+y+5z-2=0.…

Q: 24. The plane that contains the line x = 1 + t, y = 2 – t, z = 4 – 3t and is parallel to the plane…

A: To find out equation of plane first we change the equation of line in symmetrical form then find out…

Q: Find the point where the given line intersects the given plane x = 1-t, y = t, z = 1+t, z = 1- 2x +y

A: Given lines, x=1-t , y=t  , z=1+t  Given plane, z=1-2x+y To find the point where the given line…

Q: Verify Green's theorem in the plane for M = -2y and N = x , where C is the semi circle x2 + y? = 9,…

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Q: Find the distance between the given point and the given plane. Point: (−1, 4, −2) Plane: x+2y+z=3

A: We can use distance formula to calculate the distance.

Q: 34. Find the points where the line y = 2x intersect a circle of radius 6 centered at the origin.…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Find the acute angles between the intersecting lines x = 2 + t, y = 4t + 2, z = 1 + t and x = 3t -…

A: Given: The equation of lines x = 2 + t,  y = 4t + 2,    z = 1 + t      and x = 3t - 2,   y = -2,   z…

Q: is the line x = 1 - 2t, y = 2 + 5t, z =-3t parallel to the plane 2x + y - z = 8? Give reasons for…

A: Given,

Q: Find the length of the curve. 2,3/2,0 st s9 x= 4t, y 3 61 242 2 3 O 2. seçenek 4. seçenek 122 61 3 3…

A: We can find the arc length as below

Q: Find the distance from the point (1,1,5) to the line X=1+t, Y=3-t, Z=2t. O (5)^0.5 O 7 O 2(3)^0.5 O…

A: Given: Equation of line is: X = 1+ t Y = 3 - t Z = 2t To find: distance from the point (1, 1, 5) to…

Q: Is the line x = 4+ 2t , y =-t , z = -4t – 1 parallel to the plane 3x + 2y + z = 7? %3D

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Q: 12) Find the intersection of the plane: x – z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

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Q: A plane can be determined by points, that are not on the same line. OA. unable to be determined OB.…

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Q: e. The plane through Po(2, 4, 5) perpendicular to the line x = 5+ t, y = 1 + 31, z = 4t

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Ex: Find egns of the line thru the pt ( -!,), perpendicular bo the line 3x= 2y == and paralled to…

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Q: 1 Identify the statement as true or false and justify your answer. If m is perpendicular to plane T…

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Q: 8) Determine if the line given by r(t) = intersects the xz-plane. If so, determine at what point.

A: we have to find the point of intersection.

Q: Find the acute angles between the intersecting lines x = t, y = 2t, z = -t and x = 1 - t, y = 5 + t,…

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Q: The distance from the point P(2, 1, 0) to the plane 2x + y + 2z+ 6 = 0 is 3.7 True O False

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Q: 3. Determine the angle between the planes: x - z+7=0 2x +y-z+8 = 0

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Q: what is the intersection of plane  x+2y+z=0 and the line (x,y,z)=(0,1,2)+k(–1,1,2), KER(real…

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Q: Let y = [3] and u = [2] to the line through u and the origin. Compute the distance from y

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Q: the plane whose intercepts with X zagy = b,Z=C show that the Coordinate axes are has equation Ą + +…

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Q: Find the distance between the plane x+y +z = 3 and the line L= λ(1,0,-1).

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Q: 8. What is the angle between the two planes x+y=0 and y-z=2?

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Q: Find the point at which the line 7(t) = +t intersects the xy plane. %3D

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Q: What is the intersection of the plane x+2y-z=0 and the line (x.y,z) = (2,2, - 3)+ k(4,–1,1), kER?…

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Q: Find the angle between the line 2 x+v3 : = z + 1 and the plane vZx + y + z – 2 = 0.

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Q: ind the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y –…

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Q: Q2. A. Show that the plane 3x +y- z = 9 and the line {x 2,y =-1+ 3t,z 1+ 3t} are parallel, then find…

A: Answer