Find the parametric equations for the line through the point P=(-5,4,-1) that is perpendicular to the plane 2x-1y-5z=1. Use 't' as your variable, t=0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane. a)X=? b)y=? c)z=?

Q: Is the line x = 9- 8t, y= 4 + 2t, z= - 5t parallel to the plane 2x + y-z=2? Give reasons for your…

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Q: Find the real number a such that the line of x = 1, y = 2-1, z=3+t, the plane of equation parametric…

A: Given parametric equations are x=t , y=2-t, z=3+t Where t∈ℝ and  Plane is αx+5y+z-10=0

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 through (- 1,6, - 1) perpendicular to the plane 7x+ 5y + 5z =…

A: to find the parametric equations for line passing through (-1, 6, -1) and perpendicular to the…

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 parametric equations for the lines. Where, the line through the point P (3, -4, -1)…

A: Topic = Vector

Q: Find parametric equations for the lines in The line through the origin parallel to the vector 2j + k

A: Given  The vector equation is  0i +2j+k  The line passing through origin , origin is  ( 0 ,0 ,0)…

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 parametric equation for the line in R' that passes through the point (1, –2, 3) and that is…

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Q: Find parametric equations of the line through (-3,0, 4) that is parallel to 5i– 8j+k. x(t) y(t) =…

A: Parametric equations of a line passing through the point P(a,b,c) and parallel to the vector v→=…

Q: Find the parametric equations of the line through the point P(1, 2, 4) and parallel to the vector .

A: use the parametric form  of line .

Q: Find parametric equations for the line whose vector equation is given. (а) (т, у) 3 (6, —5) + t(1,…

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Q: Give a vector parametric equation for the line through the point (4, 2) that is perpendicular to the…

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Q: Find a parametric equation for the line through the point (6,5, - 3) and perpendicular to the plane…

A: Given plane is, 7x+4y+4z=15 Since, the line is perpendicular to the plane then the normal vector…

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: Complete the parametric equations for the line where the planes – 8z – 2y – 5z = 0 and - 4x + 2y –…

A: Given: The planes are -8x-2y-5z=0 and -4x+2y-9z=0 To find the parametric equation xt, yt, zt

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

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Q: Find the parametric equations for the line through the point (5, 2, 9) and perpendicular to the…

A: The parametric equation of a line passing through the point and has a direction cosines <a , b…

Q: Complete the parametric equations for the line where the planes 8x + 11y + 4z 13x + 2y + 3z = 5…

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

Q: Find a parametric equation for the line through the point (2,3, – 1) and perpendicular to the plane…

A: Given that The point on the line (2,3,-1) and perpendicular to the plane 8x+3y+3z=5 A vector…

Q: Find parametric equations of the line through (–3, 0, 3) that is parallel to 5i – 8j+ k. x(t) y(t)…

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Q: Find the parametric equation of the line of intersection of two planes correctly: P1:x+3y+5z=0 and…

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

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Q: Find the parametric equations for the line through the point (1, 7, 2) that is parallel to the plane…

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

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

A: We have to write a parametric equation of the line  which is passing through the point (-1, -1)…

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: The unit vector normal to the plane 2x + 3y + 6z = 7 is

A: The given plane is 2x + 3y + 6z=7. The unit normal vector to fx,y is defined as n=∇F∇F. The normal…

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: Give a vector parametric equation for the line through the point (-2, –2) that is perpendicular to…

A:

Q: Give a vector parametric equation for the line through the point (1,−4,1) that is parallel to the…

A: We have to find the vector parametric equation for the line through the point (1,-4,1) that is…

Q: The planes 3x−4y+5z=−28 and 4x−2y+4z=−24 are not parallel, so they must intersect along a line that…

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q, given P(0,…

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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 for the line whose vector equation is given. (а) («, у) %3D (3, —3) + t(1,…

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Q: R(u, v) = (uv, u sin v, v cos u)

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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: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (4, –3) +t(1,…

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Q: Suppose a line is given parametrically by the equation L(t)=(1-t, t-4, 1-t) then the vector u and…

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Q: Find a vector parallel to the line defined by the parametric equations x(t) - 3 – 9t y(t) 2 + 7t…

A: Need to find parallel vector and point on the line

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

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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

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.