Let / be the line given in parametric form by the equations x = 3 +72 y = 0+32 z = -1+ 22 What is the distance between the origin and the line /?

Q: Find parametric equations for the line passing through the points (10,3,1) and (8,6,-2) using the…

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Q: Find the length of one arc of the curve whose parametric equation are x=2θ-2sinθ and y=2-2cosθ.

A: We have to find length of arc whose parametric equations are : x=2θ-2sinθ and y=2-2cosθ Suppose 0 ≤…

Q: Calculate the distance between the points J (-7,0) and L= (-2,-4) in the coordinate plane. Give an…

A: Given,            Two points J(-7,0) and L(-2,-4) in coordinate plane we need to calculate distance…

Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it.

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Q: Find the parametric equation of the line ( x-3, y+6 )•( 2,-3 ) = 0

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Q: Find parametric equations for the line formed by the intersection of planes x + y - z = 29 and 3x -…

A: Consider the given:…

Q: Find the parametric equation of the lines passing through (4, -2, 5) and (-3, 0, 6)?

A: Consider the two given points (4,-2,5) and (-3,0,6). The objective of the problem is to find the…

Q: Give the parametric and symmetric equations of the line that passes through the point (4, –3, 5) and…

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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 a parametric description of the line segment with endpoints P(-1,3) to Q(3,-2)

A: The line segments with endpoints P(-1,3) to Q(3,-2)

Q: Consider the point (3,4,5) What is the projection of the point on the xy-plane?

A: The given point is (3,4,5).

Q: Find parametric equations for the line segment joining the points (-7, 6) and (5, 3). x=-7+12t, y…

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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: Find the parametric equations for the line segment from (5,-1,1) to (5,4,3)

A: The given points are 5, -1, 1 and 5, 4, 3. The parametric equation of a line segment joining the…

Q: Determine the parametric and symmetric equation of line passing through the points (1, –3,2), (5,…

A: To find the parametric and symmetric equation of line passing through the points (1,-3,2) ,(5,-2,8)…

Q: Find the point-normal form equation of the plane containing the point (1, -3, 5) and the line with…

A: Solution: P(1 , -3 , 5) (2 - x ) = (y+1)/2 = -z/3 = t

Q: Find parametric equation of the line passing through point (4,2) and parallel to vector 7 = -i+5j.

A: Given: A line passes through the point (4, 2). The line is parallel to the direction vector…

Q: Find the parametric equation of the line through the points (−3, −2, 1) and(−1, −3, −1)

A: Given:

Q: Find a set of parametric and symmetric equations of the line satisfying the following Passing…

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Q: Find the parametric equation for the line through the point (2,-3,1) and parallel to the vector…

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Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it using…

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Q: Find parametric equations for the lines with the given description. Parallel to the line through (1,…

A: Consider the given points 1,1,0 and 0,-1,-2 Passes through the point 0,0,4

Q: Suppose a line is given parametrically by the equation L (t) = (1- 3t,3t – 4, -3-t)- Then the vector…

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Q: Find a set of parametric and symmetric equations of the line satisfying the following Passing…

A: We have to find the equation of the line passing through the point (1,2,-1) and normal to the plane…

Q: Find parametric equations for the lines in The line through P(-2, 0, 3) and Q(3, 5, -2)

A: To find the parametric equation for PQ

Q: Give the parametric and symmetric equations of the line that passes through the point (4, –3,5) and…

A: we have to find the equation of line which is passes through the given point and perpendicular to…

Q: Line 1: 1 - y = Z – 8 2 х — 3 4 Line 2: x=-2t y=2+2t z=6+2t 1.If the given lines intersect at a…

A: To find the given questions when two lines Line1 and Line2 are given :-

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 for the line that passes through the point  (5, 2) and is parallel to the…

A: we have to find parametric equations for the line that passes through the point  (5, 2) and is…

Q: I need to get the parametric equation for a line between the points (0,1,2) to (3,0,-1). I have the…

A: Line passing though the points 0, 1, 2 & 3, 0, -1. Now let, x0, y0, z0=0, 1, 2 & x1, y1,…

Q: Find parametric equations for the lines in The line through (1, 1, 1) parallel to the z-axis

A: Given: 1,1,1 parallel to z-axis

Q: Find Parametric efuatins for the lines - The line through (1-2-2) Paralle tothe(Z)-axis.

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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: 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: y+3x-6z=8

A: answer is in next step

Q: What are the direction numbers of a line given by the parametric equation:  x=6+t,y=5+4t,z=1−2t

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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 for lines passing through point Pand parallel to vector n: (а) Р(3, — 1,…

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Q: Find parametric equations of the line passing through (3, −1, −3) and perpendicular to the line…

A: The required line is passing through the point 3,-1,-3 and is perpendicular to 3,-2,4 and 0,3,5.…

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: Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line…

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Q: Find parametric equations of the line through (-3,1,1) that is parallel to 2i – 5j+k. -

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Q: Determine the parametric equations of the path of a particle that travels the circle:

A: Given,        (x-4)2+(y-3)2=49 Time interval is 0≤t≤2π

Q: Give the parametric and symmetric equations of the line that passes through the point (5,−1,3) and…

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Q: Find the distance between the point (4, −1, 5) and the line given by the set of parametric equations…

A: The point is: P(4, −1, 5) The line is: x = 3, y = 1 + 3t, z = 1 + t The line is: <3, 1, 1> +…

Q: Find the parametric equations of the line that is perpendicular to the plane 2x +y +3z = 4 and goes…

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Q: Let L be the line with parametric equations

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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.