When finding parametric equations for the line of intersection of two given planes, how do we use two equations (one from each plane) and three unknowns to have a free variable and parameterize the line of intersection? Please do an example with planes x + y + z = 1 and x + 2y + 2z = 1, and explain each step carefully and use typefont. Thank you!

Q: the plane curve described by the parametric equations x=cost and y=3sint has a counter-clockwise…

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Q: Find parametric equations for the curve with the given properties. The line passing through (5, 7)…

A: Given that the line is passing through (5, 7) and (6, 8) So the direction vector of this line is:

Q: 4. Find parametric equations of a line passing through (1, 2, 3) that is parallel to the plane…

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Q: Find parametric equations for the line that passes through the point  (−3, 7) and is perpendicular…

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Q: Select a parametric equation that represents the line that passes through the points (3,0,−2) and…

A: Find the direction vector of the line using the two points

Q: True or false: There is more than one way for pairs of parametric equations to represent the same…

A: There is more than one way for pairs of parametric equations to represent the same plane…

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

A: Given: Point (-6, -8, 2) and plane: xz-plane  To Find: Set of parametric equations of the line…

Q: Find parametric equations of the line of intersection of the two planes. 9x + 8y - 9z = -3, -7x - 5y…

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Q: Find symmetric and parametric equations of the line through the two points (−3, 5, 2) and (1, −3,…

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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.…

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Q: the line satisfying the given conditions. If possible, also indicate the symmetric equations. line…

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Q: Find parametric equations for the line of slope 2 that passes through the point (3, 5)

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Q: Find parametric equations of the line that satisfies the stated conditions. The line through (8, 6)…

A: Given;  The line through (8,6) that is parallel to -4i+3j.

Q: Write parametric equations of a line that goes through the point (-1, 1, -1) and tangent to the…

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Q: Find a parametric equation for the line

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Q: Construct parametric equations describing the graph of the line passing through the following…

A: Topic = Coordinate geometry

Q: Please help me with this precalc homework question

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Q: Find parametric equations for the intersection of the surfaces y = x² and 2x² + y² + 6z² = 24 and…

A: Find out the parametric equations for the intersection of the surfaces y=x2 and 2x2+y2+6z2=24…

Q: 5. Find parametric equations for the line through the points (1, 3, 0) and (2, 4, 4).

A: 5. Given that, the points are 1,3,0 and 2,4,4. Note that, the symmetric equation of the a straight…

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: 2: (a) Find parametric equations for the line through the point (-6, 1,2) and the point of…

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Q: find parametric equations for the lines with the given description.  Passes through (1, −1, 0) and…

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Q: Find the parametric equation and symmetric equations for the line passing through the points (2, –2,…

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Q: Find parametric equations for the line described below. The line through the point P(7, -4, 0) and…

A: NOTE: Refresh your page if you can't see any equations. . the given plane is  the normal vector is…

Q: A line with parametric equations x = 10 + 2s, y = 5 + s, z = 2, seR, intersects a sphere with the…

A: The solution of given problem as follows :

Q: Find a parametric equation for the line through the point (6,2,3) and in the direction of ai⃗ +bj⃗…

A: Given: (6,2,3) Direction=ai+bj+ck

Q: Find a set of parametric equations and symmetric equations of the line ` con- taining the point P(1,…

A: Given Point is (1,-2,3) And Plan is : 2x-y+3z=6

Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

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Q: Find parametric equations for the line in which the planes, X+2y-2z=5 and 5x-2y-z=0 intersects. Show…

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Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

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Q: Find parametric equations for the line through (-4,1,1) parallel to the x-axis. Let z = 1. y-z=…

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Q: Eliminating the parameter means algebraically eliminating the variable _______ from a pair of…

A: The objective is to fill the blanks Eliminating the parameter means algebraically eliminating the…

Q: Find parametric equations for the line of slope 2 that passes through the point 13, 52 .

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

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Q: Find parametric equations for the line through the point P(2,3,4) parallel to the plane -x+5y-6z=10…

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Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

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Q: Find parametric equations for the line through the point (0, 1, 2) that is parallel to the plane x +…

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Q: 9. Find a parametric equation for the line that is orthogonal to the surface 2 at the point (1, 1,…

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Q: 5. Find the parametric equations of the line through A (-1, 2, 3) and B (2, 2, -3). Hence find where…

A: The set of parametric equations of a line passing through the points (x1,y1,z1) and (x2,y2,z2) are…

Q: Find parametric equations for the line segment joining the points (-6, 7) and (4, 5). x=7-2t, y…

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Q: A line with parametric equations r = 10 + 2s, y = 5 + 5,2 = 2, sER, intersects a sphere with the…

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Q: Find a set of parametric equations for the rectangular equation that satisfies the given condition.…

A: Given

Q: Find parametric equations and a parameter interval for the motion of a particle in the xy-plane that…

A: It is known that,

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: Find parametric equations of the line through the given points. (a) (2, −3, 1), (4, 2, 5) (b) (−3,…

A: The parametric form of a line passing through two points px1,y1,z1 and Qx2,y2,z2.Fix P-base…

Q: Write parametric equations for the line that passes through the point P ( 0 , 4 , 0 )  at time t = 0…

A: Given points are, P=0,4,0 at t=0Q=-3,10,15 at t=3 Let, the vector line be, rt=u→+tv→At the point P,…

Q: Find the equation for the plane that passes through (2,4,-1) and contains the intersection of the…

A: The plane equation Ax+By+Cz+D=0 passing through three points x1,y1,z1, x2,y2,z2 and x3,y3,z3 is…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.