What is the parametric equations of the line through (2,2,2) parallel to the x- axis ? a) x = 2, y = 2 + 2t, z = 2 c) x = 2+ 2t, y = 2, z = 2 b) x = 2, y = 2, z = 2+ 2t d) x = 2,y = 2, z = 2

Q: Lo and Li are lines in 3-space whose parametric equations are Loix = x0 + aot, y = yo + bot, z = zo…

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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: 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: The parametric equation of the line resulted from intersection of x-y 0, and z = 2 is %3D

A: Use the given planes.

Q: Find parametric equations for the line going through (5, 4, 6) and is perpendicular to the plane x −…

A: Here, By substituting the values of r0 and v in vector equation,

Q: Find a set of parametric equation of the line through the point (-2, 0, 3) parallel to the vector v…

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Q: Find parametric equations of the line through (-3,0, 3) that is parallel to 5i– 7j+k.

A: Recall:  The parametric equations of the line through (x0,y0,z0) that is parallel to a i+b j+c k is…

Q: Find parametric equations of the line through the point (8, 3, 4) that is parallel to the plane -2x…

A: First find vector normal to plane Write equation of line

Q: A parametric equation of the line of the intersection of the planes x - z = 0 and x – y + 2z = 0 is

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Q: Find the set of parametric equations of the line through the point (1, 6, 3) that is parallel to the…

A: The direction ratio of the line x=6+5t, y=6+2t, z=4+2t is (5,2,2). Parallel lines have the same…

Q: Find the distance between the point (1, −2, 4) and the line given by the set of parametric equations…

A: The given point is M=(1, −2, 4) The direction vector of the line is =s=(2,1,2) A point on the line…

Q: Find the parametric equations for the line in the x-y plane which goes through the points (2,-1) and…

A: The parametric equations for the line in the x-y plane which goes through the points (2,-1) and…

Q: In Exercises 23–38, find parametric equations for the given curve. 30 31. Line through (3, 1) and…

A: Consider the points of line, (3, 1) and (-5, 4) To calculate the equation of line passing through…

Q: Find a set of parametric equations for the line passing through the point (8, 0, 9) that is parallel…

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Q: Choose the parametric equations that represent the line segment that goes through the points (1,4,…

A: Given points x0,y0,z0=(1,4,-5) and x1y1,z1=(2,2,-1)

Q: I am working with cal 3. How do I find the parametric equations of the line for the intersection of…

A: The parametric equations of a line through the point (x0, y0, z0) and parallel to the direction…

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

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Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

A: The objective is to find the parametric equations of the line through the point.

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: In Exercises 23–38, find parametric equations for the given curve. 30. Line through (2, 5)…

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Q: The angle and the parametric equations for the intersect line between planes a + y = 1, and 2r+y-2z…

A: Given, x+y=1, 2x+y-2z=2 we know angle between two plane is…

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: ) (i) Find the parametric equations for a smooth curve, C: x= 4z, y = -3z that joins two points,…

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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 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: Consider the point (−6, 2, 2), line l : (1 − x)/7 = y − 3 = z/2. Find parametric equations of the…

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Q: Find the symmetric and parametric equation of the line that is the intersection between the planes…

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

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Q: Find parametric equations for the lines in The line through the point (3, -2, 1) parallel to the…

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Q: Find the parametric equations for the line through the point P = (-1, 4, -4) that is perpendicular…

A: Normal vector perpendicular to the plane 2x−4y−2z=1 is: (2, -4, -2) The line passes through P = (-1,…

Q: What is the parametric equation for the line through the point (1,2, 3) paralkel to the y- axis? (a)…

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Q: Write the parametric equations of the line through the point P (-6, 4, 3), that is perpendicular to…

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Q: Find parametric equations of the line through the point (8,3, 4) that is parallel to the plane -2x +…

A: The parallel line through the point has the vector equation L = < 8,3,4 > + t < a, b, c…

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: The angle and the parametric equations for the intersect line between planes a+y = 1, and 2r +y - 2z…

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

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Q: The angle and the parametric equations for the intersect line between planes x + y = 1, and 2x + y–…

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Q: Find the distance between point A(3, 4, 4) and the line of parametric equations x = -1-t, y = -t, z…

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Q: The line L is parallel to the plane x+y+z=2 and is perpendicular to the vector (-1,1,–2). If the…

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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.