Q1: Find the parametric rquations of the line that passes through the point P(4,2,-3) and Q(-3,2,2). At what point does the line intersect the xy-plane?.

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: Find parametric equation for the lines .. The line through (0, -7, 0) perpendicular to the plane x +…

A: A parametric equation of a line can be written if a point on the line is given and a vector parallel…

Q: Find parametric equations for the line through (7,4, – 7) perpendicular to the plane 4x + 5y + 4z =…

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

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Q: Find parametric equations for the normal line to the surface z=-7x2 -9y2   at the point   (2,1,-37)

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

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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 line that passes through point P(2,3,4) and is perpendicular to…

A: To Determine: Find the parametric equation of the line that passes through point P(2,3,4) and is…

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 given curve. y = x2, translated so that the minimum occurs at…

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Q: 8. Find a parametric representation of the line through the point P(1,0,4) and perpendicular to the…

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Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2,4) and (-…

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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: Find parametric equations for the line segment joining the points (9, 8) and (16, 11). O x=9+7t, y…

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Q: Find a parametrization of the curve. The vertical line passing through the point (3, 2, 0)

A: Consider the given point  3 , 2 , 0

Q: Find the distance from the point (−5,2,−3) to the (a) xy-plane (b) xz-plane (c) yz-plane (d) x-axis…

A: We know that distanced of xy-plane from the pointx0,y0,z0 is given by d=z0…

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

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Q: Q5] What is a parametric representation of a curve? What is its advantage?

A: We are entitled to solve only one question at a time so we will answer only the first question.…

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: For which values of t is the parametric curve x=8t, y=t+t, -0c0s ts 00 concave up? (Enter your…

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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: Find parametric equations of the line through the point (5, 0,−2) that is parallel to the planes x…

A: Any point in three dimensional coordinate system will be of the form x1,y1,z1 . We can calculate the…

Q: Find the length of the parametric y = 2 , - V3sts V3. curve x = 1+

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Q: What are the parametric equations for the intersection of the planes x - y - z = 1 and 2x + 3y + z…

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Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 3x + 4y +…

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

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Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 2x + 4y +…

A: Equation of line normal to graph of functions f(x) is :  r<t> = <x0,y0,z0> +…

Q: Find the parametric equation for the line where the planes 4x – by + 8z = - 36 and – by + z = – 15…

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Q: Find the slope of the parametric curve x = -2t3 + 1, y = 3t2, for - ∞ < t < ∞, at the point…

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Q: 6. Find parametric equations for the line of intersection of the planes 2x – y + z = 4 and 3x + y +…

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Q: iminate the parameter in x = -t +2t and y =t-4 and then identify the parametric sketch its image in…

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Q: Find parametric equations for the line pass- ng through the point P(1, –1, 3) and perpen- licular to…

A: Given that: Line is passing through P(1,-1,3) and perpendicular to the plane:       4x+3y-2z=6.

Q: Q.1 Find the parametric equation of the line that 2)Passes point (1,3,7) and orthogonal to xy-…

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Q: Find parametric equations for the line segment joining the points (-6, 4) and (2, 3). x=-6 + 8t, y =…

A: Parametric equation of line segment.

Q: Find the parametric equation of the line tangent to the curve of intersection of the cylinder…

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Q: Find the parametric equation of the intersection of the planes x + y = 1 and x + z = 2.

A: Equation of plane 1 - x+y = 1        Normal vector of plane 1 = n1 = 1,1,0…

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

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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: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8…

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become:

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 4x+2y…

A: Let F(x,y,z) define a surface that is differentiable at a point (x0,y0,z0), then the normal line to…

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 4x + y +…

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Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y2 = 8 ,…

A: We have given the surfaces; And the point (2,2,8)

Q: Find parametric equations for the line through the point (0, 1, 3) that is perpendicular to the line…

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Q: Q. Find parametric equation of the line perpendicular to the lines l1: x = 1- 1, y=t, 12 : z = 2t –1…

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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 line through the point (0, 1, 2) that is perpendicular to the line…

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Q: Flnd the parametric equation of the line of ntersection of the planes and

A: First find normal vector then take cross product and use formula

Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y² = 8 ,…

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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: 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