6. (a) Find parametric equations for the line through A = (1, 2, 3) and B = (0, 2, 2). (b) Find the intersection between that line and the sphere of radius 3 centers at the origin. %3D

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

A:

Q: parametric

A:

Q: find a parametric equation for the line that is per-pendicular to the graph of the given equation at…

A: 41. Here the given as  Now we let

Q: Find a rectangular equation for the plane curve defined by the parametric equations. x==° +1,…

A:

Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations x…

A: Given: x=4 costy=2 sin2tt=π3

Q: find parametric equations for the given curve.  Line through (2, 5) perpendicular to y = 3x

A: Find parametric equations for the given curve.  Line through (2, 5) perpendicular to y = 3x

Q: Find parametric equations and a parameter interval for the motion of a particle that starts at the…

A:

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

A: Consider the given:…

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: Suppose parametric equations for the line segment between (-2, 10) and (8, 9) have the form: a + bt…

A: Note: As per our company guidelines we are supposed to answer the first question. Kindly ask the…

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

A:

Q: Find parametric equations and a parameter interval for the motion of a particle starting at the…

A: Given,

Q: 14. The curve represented by parametric equations x = 4cose and y 4sine is a

A:

Q: 7. Sketch the curve with parametric equations z =e, y =e', teR.

A:

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A: Given that z=x2+y2 and 3x−5y+7z=24 and point is 3,4,5. Let fx,y,z=x2+y2−z and gx,y,z=3x−5y+7z−24 We…

Q: A particle moves in space along a path whose parametric equations are given by x1 = b sin(wt), x2 =…

A:

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

A:

Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y? = 8,…

A: Given: The parametric equations for the line tangent to curve of intersection of the surfaces…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

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

A:

Q: find a parametric equation for the line that is perpendicularto the graph of the given equation at…

A: We have to find parametric equation for the line that is perpendicular to the graph of the given…

Q: Find the distance from the point (3, 2, 5)to the line with parametric equations x=t,y =l +t ,z = 2 +…

A: The equation of the line in matrix form:                                                xyz = 012 +…

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

A: The given equation of circle at (a,0) is The general parametric equation of circle is where x,y…

Q: Find parametric equations and a parameter interval for the motion of a particle that starts at (a,…

A:

Q: find parametric equations for the lines with the given description.  Perpendicular to the yz-plane,…

A: To find parametric equation perpendicular to yz plane passes through (0,0,2)

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

A:

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

A:

Q: 4. Sketch the parametric equations by eliminating the parameter. Be sure to include arrows to…

A: From given equations, we find sin theta and cos theta Then we plug them in the Pythagorean identity…

Q: Find parametric equations of the line containing the .point (2, 3,-1) and normal to the plane x+…

A:

Q: Find parametric equations for the path of a particle that moves along the curve y=x from (1, 1) to…

A: Given Parabola is y = x²

Q: Find a parameterization for the line segment joining points (0,3) and (12,0) using the angle 0 in…

A:

Q: Find an equation of the circle with center at (-4,1) that is tangent to the y-axis in the form of…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

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: Sketch the curve represented by the parametric equations (indicate the orientation of the curve). x…

A:

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

A:

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

A:

Q: Explain how a pair of parametric equations generates a curve in the xy-plane.

A: Our Aim is to explain the fact that how a pair of parametric equationsgenerates a curve in the…

Q: Find set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A:

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: Given, the surfaces:               x+y2+2z=4,   x=1  Point: (1, 1, 1) Let         z = 1-2t

Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve). x…

A:

Q: 5. Sketch the parametric curve x = t2 – t, y = t³ – 3t and determine the location (x, y and t) where…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

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

A:

Q: 7. Sketch the curve with parametric equations x = e-t , y = e', teR.

A: Topic = Functions

Q: Find parametric equations for the line formed by the intersection of planes x+y-z=3 and 3x-y+3z=5.

A: First we find a point on the intersection of these planes with the plane z=0. And next find the…

Q: find parametric equations for the given curve. Segment joining (1, 1) and (2, 3)

A:

Q: Find parametric equation of a helix radius 5 from a point (5, 0 ,0) to a point (0, 5, 1)

A: Given that the radius of the helix is R=5. We know that the parametric equation of helix is given…

Q: 3) (i) Eliminate the parameter to find a Cartesian equation of the curve. (ii) Sketch the parametric…

A: Our objective is to eliminate the parameters to find the cartesian equation of the curve and sketch…

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: 1) Find the parametric equations of the line that is tangent to circle x² + y² = 25 at point (3, -4)

A: Given, Equation of circle: x2 +y2=25 at a point (3,-4). now, parametric equation of the line is…