Find a parametric representation of the line of intersection of the two given planes 2x+y-z=6 x+2y+z=9

Q: Let S be the plane with equation 2x - 3y + 4z = 1. Find parametric equations of a line that goes…

A: Explanation of the answer is as follows

Q: Let A : x + 2y – z, B be the plane passing through the points (2, 1, 2), (1, 1, 3), (2, -1, 1), and…

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Q: fficients of x, y, and z in the given equation of the plane. ..... z= -7+ 9t. pe expressions using t…

A: Find parametric equation.

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-4, 0,…

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Q: Find the angle between the two planes x − 2y + z = 0 and 2x + 3y − 2z = 0. Then find parametric…

A: The equation of two planes are x-2y+z = 0       ...... (1) 2x+3y-2z = 0   ...... (2) Angle between…

Q: Consider the plane that goes through the point (4, 1, 3) and is orthogonal to vector (2, 3, 1). Find…

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Q: Find a set of parametric equations of the line with the given characteristics. The line passes…

A: Given: Point (2, 3, 4) and plane 3x + 2y − z = 6. To Find: Equation of the line passing through the…

Q: Q1: Find the parametric rquations of the line that passes through the point P(4,2,-3) and Q(-3,2,2).…

A: Here we have to find the parametric equation of the line that passes through the point P(4,2,-3) and…

Q: Choose the parametric equations of the line of intersection of the planes. For the point on the…

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Q: Consider the planes of equations −y+z−2=0 and x−y=0. a) Show that the planes intersect. b) Find…

A: We can solve this using definition of intersection of plane

Q: Consider the planes of equations -y+z - 2 = 0 and x- y = 0. a. Show that the planes intersect. b.…

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Q: गाण the Simultaneous earvation. ntuy-4 the linel in ay Plane and indiceate the solu tion.

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Q: Find an equation of the sphere with center (1, -8, 3) and radius 5. (x – r- 1)² + (y + 8)² + (z –…

A: Given: Center of the sphere (1, -8, 3) and radius of the sphere is 5. To describe: The intersection…

Q: Use this method to find the line of intersection of the plane x + 2y + 3z = 6 and the plane x + y +…

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Q: Find a parametric representation for the surface. The part of the plane  z = x + 2  that lies…

A: Given: The part of the plane  z = x + 2  that lies inside the cylinder  x2 + y2 = 9.

Q: 52. The plane passing through the point P,(0, 2, -2) that is parallel to the plane 2x + y-z= 1

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Q: 20. Find the coordinates of the point where the line with parametric equations x =1-1, y=3+t, z=3-21…

A: If they intersect the XOZ plane then the value of y coordinate is 0.

Q: Find a set of parametric equations for the line passing through the point (7, o, 9) that is parallel…

A: Parametric equation of line in 3D

Q: Find a parametrization of the line in which the planes x + 2y - 2z= 3 and 2x+ 3y - 3z = 5 intersect.…

A: Given , The equation of two planesx+2y-2z=32x+3y-3z=5for the plane x+2y-2z=3Normal…

Q: Find a set of parametric equations of the line with the given characteristics. The line passes…

A: We have to find a set of parametric equations of the line with the given characteristicsThe line…

Q: Three planes fly in specific directions as shown below. Is there a possibility of a collision…

A: If any two planes collide, then, they will be at a same point at collision, i.e., there coordinates…

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

A: We need to find the vector equation of the line of intersection. In order to get it, we’ll need to…

Q: Find a parametrization of the line in which the planes x-2y-2z = 1 and 4x - 3y - 3z = -6 intersect.…

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Q: A solid E is made up of a cylinder, with radius 3 units and height 4 units, and a hemisphere…

A: Question 5   A solid E is made up of a cylinder, with radius 3 units and height 4 units, and a…

Q: Determine the parametric equations of the plane containing the point (1, -5, 9) and the line [x, y,…

A: I am going to calculate the parametric equations of the plane containing point (1,-5,9) and the line…

Q: Find a set of parametric equations for the line passing through the point (4, 0, 7) that is parallel…

A: topic - equation of a line

Q: what is the sum of a+b+c of the intersection of the plane and line parameterized by x=r, y=1+r,…

A: A plane perpendicular to a vector and through a point In vector form, a plane's equation is…

Q: Consider three planes P, Q and R in R3 (a) Explain in words what the intersection of P, Q and R can…

A: Let P, Q, R be the 3 planes in space. We have to study the cases of the intersection of them.

Q: Find parametric equations for the line through the point (0, 2, 2) that is parallel to the plane x +…

A: Here we have to find the parametric equation of the line through the point 0,2,2 that is parallel to…

Q: . [V] Find a parametrization of the plane that contains both the point (2, 4, 6) and the line x = 7…

A: Equation of the plane  a(x-x0) + b(y-y0)+c(z-z0) = 0

Q: A solid E is made up of a cylinder, with radius 3 units and height 4 units, and a hemisphere…

A: Question 5 A solid E is made up of a cylinder, with radius 3 units and height 4 units, and a…

Q: 1. Define solid geometry and plane geometry. 2. Differentiate solid geometry from plane geometry. 3.…

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Q: Find parametric equations of the line that satisfies the stated conditions. The line through (– 8,…

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Q: Find a set of parametric equations for the line passing through the point (7, 0, 2) that is parallel…

A: We are asked to find the equation of the line.

Q: Find a parametrization of the line in which the planes x+ 4y + 2z = - 1 and 3x + 6y + 3z = 3…

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Q: 2. Use parametric equations to derive the formula for the lateral surface area of a right circular…

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Q: The Line LI : %3D Plane X+ 3y-Z= -3 , P and intersect the %3D Lind the point of intersection Irne in…

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

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Q: Find a parametrization of the line in which the planes x + 2y - 2z = 1 and 3x + 3y – 3z = 0…

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Q: Find a set of parametric equations for the line passing through the point (1, 0, 2) that is parallel…

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Q: 6. Find a parametric representation of the line of intersection of the two given planes. 2x+ y- z= 6…

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Q: Find the parametric and symmetric equation for the satisfying the given condition. 1. Through the…

A: Given : Equation of plane is y+3x-6z=8i.e. 3x+y-6z=8   To Find : Parametric and symmetric equation…

Q: Three planes fly in specific directions as shown below. Is there a possibility of a collision…

A: If any two planes collide, then, they will be at a same point at collision, i.e., there coordinates…

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

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Q: EXERCISE 3.4 A line segment has two ends of (-a, 0, R) and (a, 0, R). The surface of a cylinder is…

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