Find parametrizations for the line in which the planes 3r - 6y-2z = 3, and 2x+y-2z = 2 intersect.

Q: Find parametrizations for the lines in which the planes 5x - 2y = 11, 4y - 5z = -17

A: Given: The given two planes  5x-2y=11 and 4y-5z = -17 are intersects.

Q: Find the points on the surface 1x? + 3y2 + 5z2 = 1 at which the tangent plane is parallel to the…

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Q: Find the equation of the plane in the form z=c+mx+ny containing the line in the xy-plane where x=3,…

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Q: Find a parametrization for the curve described below. the line segment with endpoints (4,4) and…

A: Given,  A line segment with endpoints 4, 4  and  6, 1  We have to find the parametrization of the…

Q: Find the coordinates of the point where the line F = (1+ 2t)i + tj – 2tk intersects the plane 2x – y…

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Q: Find the distance between the point and the plane.

A: The distance of a point from a plane in the standard equation form is equal to . The given point…

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: Find a parametrization for the line segment beginning at P1 and ending at P2. 25) P1(-4, –5, 4) and…

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Q: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

A: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

Q: findthe parametríc equatlons for the line through the paint of in tersecti of the lines 4=X=2+ 36 14…

A: first we find intersection point of given line

Q: Find a parametrization of the line through P = (4, 9, 8) perpendicular to the yz-plane.

A: Equation of Linethe Line through P =(x0,y0,z0) in the diresction of vector v→=(a,b,c)is defined…

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

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Q: Find parametrizations The portion of the plane 4x + 2y + 4z = 12 that lies above the square 0<=…

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Q: Give two different parametrizations of the line through (4, 1) withslope 2.

A: Solution:GivenA point(4,1) with slope 2Formula:Equation of the line at (x1,y1)y-y1=m(x-x1)

Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2,4) and (-…

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Q: Find the distance from (−2, 4, 5) to the plane 2x + 6y − 3z = 10.

A: we know that distanced of pointx1,y1,z1 from the plane ax+by+cz=d is given by…

Q: Find the distance (d) from the point (- 4, 8, 4) to the plane 2x + 5y + 4z = - 50. d =

A: image is attached

Q: 4 Find a parametrization for the line segment with endpoints (-1,3) and (3,-2).

A: 4) To find the parametric equation of line segment with endpoints (-1,3) & (3,-2)

Q: Find the equation of the tangent plane to the paraboloid z = 2x2 +y? at the point (1,2,6). Select…

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Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

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Q: Find the Parametrization of the line.

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Q: What is the equation of the plane parallel to 3x + 4y − z = 5 passing through the origin?

A: 3x+4y-z=5

Q: Find the parametric equations for the line in which the planes x-2y+4z=2 and x+2y-2z=6 intersects

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Q: find a parametrization for the curve. the line segment with endpoints (-1, -3) and (4, 1)

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Q: Complete the parametric equations for the line where the planes - 7x + y + 3z = 3 and 4x7y + z = 23…

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Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as <1,m> vector. And point= (a,b)

Q: Find a parametric representation of the line through the point P(3,1,-4) and perpendicular to the…

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Q: Find a parametrization for the line segment beginning at P, (-5, - 2,3) and ending at P2 0, 5/4

A: We have to use parameterization of the line.

Q: Find the distance between the skew lines with parametric equations  x = 1 + t, y = 3 + 6t, z = 2t,…

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Q: Find the angle between the two planes x- 2y + z = 29, 2x + 3y – 2z = 6. And also find the parametric…

A: here we will find angle between two planes and parametric equation of plane's line of intersection,

Q: Find the distance between the point and the plane. 19. (0,0,0) and 2x+3y+z=12

A: As there are multiple questions, the first one (19) is solved here.

Q: Which of these describes a parametrized line perpendicular to the plane 3x + 2y + z = 15? A) (2 +…

A: The direction ratio of the normal vector to the plane is (3, 2,1 ) So the perpendicular line to the…

Q: Find the distance from S(1, 1, 3) to the plane 3x + 2y + 6z = 6.

A: It is given that a point S1, 1, 3 and the equation of the plane 3x+2y+6z=6   Here x1=1, y1=1, z1=3…

Q: parametrization for the line segment beginning at P1 and ending at P2. P 1(-4, 0, 3) and P 2(0, 5,…

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Q: Find the parametric equation for the line where the planes 7x – 6y + z = 10 and 2x + y – 3z = 4…

A: We have, r(t) = (0, -2, -2) + t(17, 23, 19) The detailed solution is as follows below:

Q: Find parametrizations for the line in which the planes 3r- 6y – 2z = 3, and 2x+y-2z = 2 intersect.

A: Given Equation of planes 3x-6y-2z=3 and 2x+y-2z=2

Q: Find the equation of the tangent plane to the surface 9x +36y +4z? = 108 at the point (-2,1,-3).…

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Q: Find the points on the hyperboloid 9x^2  - 45y^2 + 5z^2 = 45 where the tangent plane is parallel to…

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Q: find the (dis tan ant) between the planes ml and m2 when ml =: 3x - 2y+z = 9 and m2 =: 6x - 4y+ 2z =…

A: Consider the equation of planes m1: A1x+B1y+C1z+D1=0  m2: A2x+B2y+C2z+D2=0Two planes are parallel if…

Q: Find an equation for the plane tangent to the surface z = 2x2 - 7y at the point (3,-1,5)

A: Given surface z=2x2-7y and the point 3,-1,5. The main objective is to find an equation for the plane…

Q: Find a parametrization for the line segment beginning at P, and ending at P2. P (2,-3,2) and P2(0, –…

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Q: Give an equation of the plane whose trace in the yz-plane has equation y = 6z, and in the xy-plane…

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Q: Find parametrizations for the lines in which the planes x - 2y + 4z = 2, x + y - 2z = 5

A: Given the planes :- x - 2y + 4z = 2,  x + y - 2z = 5   The Arbitrarily set z =1 and solve the…

Q: What is the maximum height of a particle whose path has parametric equations x = t9, y = 4 − t2?

A: The height of the particle is given by it's y position: y = 4 - t2 At the maximum height, dy/dt = 0

Q: Find the parametric equation of the line of intersection of the planes 2x+y-z=1 and x-2y+3z-9

A: First find cross product take normal vector useformula

Q: Find the distance from the point B = (1,0, 2) to the plane 2P whose general equation isx + y - z =…

A: Given: equation of plane is x+y-z=1  We know that distanced from the pointx1,y1,z1 to the…

Q: Find the parametric equations for the line of the intersection L of the two planes. 6x – 3y+ z = 5…

A: Parametric equations of the line is :  x(t) = x0 + a t  y(t) = y0 + b t  z(t) = z0 + c t  Here ( x0…

Q: Find the distance from the point Q to the plane p. Q= (0, 0, 0), p with equation x - 2y + 2z = 1

A: GivenQ=0,0,0p:x−2y+2z=1