10. The point (1, 2, 5) is on the quadric surface z = x² + y². Is this point closer to the line with parametric equations x = 1+t, y=2+t, 3+t or the plane 2x + 3y +6z = 12?. You must find use distance formulas used in this class to solve this problem.

Q: Let / be the line given in parametric form by the equations x = -2 + 1A y = -1+6) z = -1+7A What is…

A: given line is                                               x=-2+λy=-1+6λz=-1+7λ any point on the…

Q: What is the distance from the point P=(2, -1, 4) to the plane 3x+5y-2z =20

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Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t,…

A: The distance from a point P(x1,y1,z1) to a plane  is

Q: Complete the parametric equations for the line where the planes - 6x - y + 11z = -34 and - 4x + 2y +…

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Q: The line ℓ is given by the equations x −2y + z = 2 and x + y −3z = 4. That is, ℓ consists of all…

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Q: For the lines: L1: x=2-4t, y= 5t, z=1+2t L2: x=-7-k, y=2+3k, z= 5+k Find the parametric equations of…

A: The line passing through the point (a,b,c) and parallel to z axis is  (a,b,c)+t(0,0,1)  That is ,…

Q: Let / be the line given in parametric form by the equations x = 1 + 21 y = -1 + 31 z = 2 + 51 What…

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Q: If (a,B.y) is a point at which the surface x2+y2-z²-2x+12=0 has a horizontal tangent plane, then y|…

A: As per guidelines, we will solve first question only. Let α,β,γ be the point on the surface…

Q: (9, - 플이 2

A: Given, the  point (r, θ, z)=(9, -π2, 8).

Q: Where does the line with parametric equations −1+3t y = 2 - 2t 2 = 3+ t intersect the plane 3x + y -…

A: Given parametric equation of line x = -1 + 3t y = 2 - 2t z = 3 + t Given plane 3x + y - 4z = -4

Q: Give a parametric representation for the straight line segment from the point (1,-1,2) to the point…

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Q: How do you find the parametric and symmetric equation of the line passing through the point (3, 2,…

A: We have to find the parametric and symmetric form of the line perpendicular to the given plane at a…

Q: A particle moves linearly from the point (- 2,4) to (10,0) in 4 seconds. Find parametric equations…

A: The given points are x1,y1=-2,4;x2,y2=10,0 So the slope is given by: m=y2-y1x2-x1=0-410--2=-13

Q: Determine parametric equations of the line of intersection of the planes x+2y+3z=4 and -2x+z=0. Then…

A: Let us consider two planes ax+by+cz+d=0 and a'x+b'y+c'z+d'=0  Intersection of two planes is line…

Q: Change the parametric equations to rectangular and then sketch an excellent graph of the rectangular…

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Q: Suppose point s in the example was at (4, 1).Would the distance between points r and s be greater…

A: In this question we have to find the distance between R at point (-5,5) and if S would have been…

Q: y -1 Q2) L, =Xx2 = -1 - 2 Fand equation of plane Canternng them

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Q: a) Find an equation of the sphere with center (1.-3,-5) and tangent to xz-plane.

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Q: Find the parametric equation for the line where the planes -7x + 7y - z = 20 and 2x + 7y + 2z = 23…

A: Please see the below steps for detailed solution.Explanation:Step 1: Given −7x+7y−z=20 and…

Q: Let / be the line given in parametric form by the equations x = -2 + 41 y = -1+31 z = -2 + 31 What…

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Q: Find the parametricequations of the line passing Through (-2,0,3) parallel to ū = 2i +49-2R.

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Q: Find the parametric equations for the path of a particle that travels three quarters of the way…

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Q: Find parametric equations for the line through Po = (10,-1, 1) perpendicular to the plane 2x + 3y -…

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Q: draw the line which start point (1,1,0) and end point (3,4,0)by using parametric equation

A: