Give a scalar equation for a plane at distance 9 from the plane P with equation -2x-2y+z = 4.

Q: Give a vector parametric equation for the line through the point (3, 1) that is perpendicular to the…

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Q: Find a parametrization of the vertical line passing through the point (9, 5, 0) using t = z as a…

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Q: Find parametric equations for the line of intersection of the planes x + 2y + 3z = 4 and 5x + 6y +…

A: Given: x+2y+3z=4   and  5x+6y+7z=8To obtain the parrametric…

Q: Find the angle between the two planes 6x − 3y + z = 5,  −x + y + 5z = 5 and find a set of parametric…

A: We have given the equation of planes; 6x − 3y + z = 5 −x + y + 5z = 5 Hence the normal vectors of…

Q: Find the standard equation of the sphere with center (−3, 2, 4) that is tangent to the plane given…

A: Radius (r) will be the distance from the center to the tangent plane. That is the distance between…

Q: Find the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: The planes 4x + 4y + 3z = -15 and y - 5x - 2z = 11 are not parallel, so they must %3D intersect…

A: Given: The planes 4x+4y+3z=-15 and y-5x-2z=11

Q: Find the vector parametric equations of the two straight lines tangent to the given space curve

A: Given,              rt=2t2+3i+15t-7j+4t2+5kand  passing through the point P-3, -22, -7.

Q: Find the ar ea of sur face x - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2,…

A: Given :          The surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x…

Q: 2. Find the vector, parametric and cartesian equation of a plane that contains the points А(-1,0,…

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Q: Find a parametrization and the equation associated with the cylindrical surface whose directrix and…

A: Use the director vector and then substitute y=0 to find the value of x and z . Then substitute the…

Q: Find a scalar equation of the plane that contains the points (−1, −3, 1), (1, 0, 3), and (2, 7, 0).

A: We are going to solve

Q: Find the distance between the point (0, 1, 2) and the plane 3x - 2y + 6z = 6.

A: Using Distance from point to plane formula,

Q: Find the angle between the two planes 3x + 2y − z = 7,  x − 4y + 2z = 0 and find a set of parametric…

A: Known fact: The angle between two planes a1x+b1y+c1z+d1=0  and a2x+b2y+c2z+d2=0 is given by…

Q: x = −1+5t y = 3-s-2t z= −2+s

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Q: Find a scalar equation of the plane containing the line x = 4+ 5t, y = 5+3t and z = 6+ 4t the point…

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Q: Find all points on the ellipsoid 2x² + 3y² + 4z² = 9at which the plane tangent to the ellipsoid is…

A: Explanation: Given that,  Ellipsoid:2x2+3y2+4z2=9Plane:x-2y+3z=5⇒15x-25y+35z=1   Suppose point of…

Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

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

A: Explanation: Given that,  Line 1: x=1+ty=1+6tz=2t Vector 1: 1,6,2 Line 2: x=1+2sy=5+15sz=-2+6s…

Q: Find a parametrization for the sphere of radius 2.

A: Consider the equation of the sphere x2+y2+z2=22. Here the sphere is centered at origin.

Q: Find an scalar equation of the plane containing the line x = 2 – 4t, y = 4 – 5t and z = 5+t and the…

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Q: Find the Parametrization of the line.

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Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: Find the equation of the XZ plane.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Explain how you would convert from a plane's scalar equation to a vecto

A: Lets understand the process of converting scalar equation of a plane to vector equation by an…

Q: Determine the scalar equation of the plane containing the point (-2, 9, 7) and 9. perpendicular to…

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Q: The planes 5x+y+z=−6 and 3y+5z=22 are not parallel, so they must intersect along a line that is…

A: Given planes are 5x+y+z=-6 and 3y+5z=22 find the vector parametric equation

Q: Find the angle between the two planes −2x + y + z = 2,  6x − 3y + 2z = 4 and find a set of…

A: The given planes are −2x + y + z = 2  and  6x − 3y + 2z = 4 . Obtain the angle between them as…

Q: Find an equation of the plane satisfying the given conditions.

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Q: What are the parametric equations for the intersection of the planes x - y - z = 1 and 2x + 3y + z…

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Q: Find a scalar (Cartesian) equation of the plane that contains the origin and the point  (2, -3, 2)…

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Q: Give the general equation of the plane satisfying the given condition. plane Σ containing the point…

A: We will find the equation of the plane Σ which is parallel to the plain 2x − 6y + 3z = 0 and…

Q: Find the angle between the two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2 and find a set of…

A: Given, two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2  we have to find the angle between the two…

Q: 5. Determine the scalar equation of the plane with x-intercept = 2, y-intercept = -1, and…

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Q: Find the standard equation of the sphere with center (-6, 2, 7) that is tangent to the plane given…

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Q: Give a vector parametric equation for the line through the point (−1,−1) that is perpendicular to…

A: Vector equation of line which passes through point r0 and perpendicular to line a+bt,c+dt is given…

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+y-2z = 3.

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Q: Give a vector parametric equation for the line through the point (4, 0, -5) that is parallel to the…

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Q: Find a parametric represent at ion for the plane that passes through the point (2, -3, 4) and cont…

A: It is asked to find the parametric form of plane that contain vectors a = < 5, -1, -2 >    and…

Q: Determine the scalar equation of the plane that passes through (5, -5, 5) and is perpendicular to…

A: Here we will find the required equation of the plane,

Q: Find a vector parametric equation for the ellipse that lies on the plane z (x + 2 - cylinder x + y =…

A: Dear student. You have posted many parts, according to the policy we will answering the first part.…

Q: Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and…

A: To find a vector function that represents the curve of intersection of the surface 4x+2y-8z2=16 and…

Q: Flnd the parametric equation of the line of ntersection of the planes and

A: First find normal vector then take cross product and use formula

Q: Find a vector parametrization for the quarter-ellipse from (5, 0, 6) to (0, −2, 6) centered at (0,…

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Q: Find a point-normal form equation of the plane containing (1, -1, 4) and line with parametric…

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Q: 10. Determine the scalar equation of a plane that is perpendicular to the line: |1,2, 3| + t|-2,4,…

A: A normal of a plane perpendicular to the line will be parallel to the line. So the plane is:…

Q: Derive the parametric equations of the line of intersection of the two planes: II : x – 2y + z =1…

A: Given: P1:   x−2y+z=1P2:   2x−2y−4z=4

Q: perpendicular

A: