Find a parametrization of the line through the origin whose projection on the xy-plane is a line of slope 2 and on the yz-plane is a line of slope 9 (i.e., Az/Ay = 9). Scale vour answer so that the

Q: 1. Prove that fo r*dr + rydy = where C1 is the line segment from (0,0) to (1,0) by using…

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Q: Find parametric equations of the normal line to the surface z = 4 +y? at the point (2, 3, 10) O x =…

A: To Find:  the parametric equations of the normal line to the surface  z = x24+y2 at the point ( 2,…

Q: a. Find a parametrization of the curve x = (y* – 3)e2y.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find parametrizations for the lines in which the planes x + y + z = 1, x + y = 2

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Q: A point moves along the intersection of the elliptic paraboloid z = 9x? + 3y² and the plane.x…

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Q: Find a parametrization for the curve described below. the line segment with endpoints (1, – 4) and…

A: Given:   Endpoint : ( 1 , -4) and ( -2 , -7)

Q: Give a parametrization, including the appropriate u- and v-bounds, for the portion a cylinder of…

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Q: What is the correct piecewise parametrization of a path C created by starting from C, of equation y…

A: Given a piecewise smooth curve C. The question is to parametrize the curve.

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

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Q: .2 y = z, -2 < z < 2 %3D (x - 2)² + 4y2 = 4

A: (b)  The given equation is y=z2, -2≤z≤2. Observe that y-coordinate will always be positive and…

Q: A point moves along the intersection of the elliptic paraboloid z = a2 + 3y? and the plane y = 1. At…

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Q: Is the below statement True or False? The parametrization for a given curve is unique.

A: No. Parametrization of a curve is not unique. For example y = x2 can be written as (t,t2) or…

Q: Find the equation of the tangent plane to the surface 2² at the point Y= 2x? (0, –1,2) %3D O y- 2z…

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Q: Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: The line joining P1,0 and Q0,1 is     x-11-0=y-00-1=t(say)⇒x=t+1,y=-t⇒dx=dt,dy=-dt

Q: Find an equation of the tangent plane to the given parametric surface at the specified point x = u?,…

A: x=u2 y=vu2 z=uv u=3 v=4 x1 =u2   x1 =9 y1 =vu2   y1=36 z1=uv z1 =12 we have to find the tangent…

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈1 − t^2, 5t, 2t^3〉, t = 2

A: r(t) =(1-t2, 5t, 2t3) at t=2

Q: Find the Parametrization of the line.

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Q: Find the slope of the tangent line at (-1, 1,5) to the curve of intersection of the surface z = x²…

A: According to question, we have, z = x2 + 4y2        .......(1)

Q: (b) Give an example of a parametrisation of the unit circle, C = {(x, y) E R² | x² + y² = 1}, that…

A: The parameterization of a circle  that generates the clockwise orientation of C is given by: x=r…

Q: Find a parametrization of the circle of radius 6 in the XY-plane, centered at the origin, oriented…

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Q: Find a parametrization of the tangent line at the point indicated. r(t) = (1 - t4, 4t, 5t), t = 2…

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Q: Find all points on the isometric dot plane, Ax,1 yl, with x and y integers, that are ex- actly V133…

A: a)The distance from origin to point x,y is 133. b)The distance from origin to point x,y is 217.

Q: 5. Are there any points on the graph of x2 - y? – 22 = 1 where the tangent plane is parallel to the…

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Q: # 3 Let act) (cost, sint a is plane Siht) %3D Decide whether not ? curve

A: Given that  α(t)==(cost,sint,sint) Now take α(t)=(x(t),y(t),z(t)) Then, x(t)=cost, y(y)=sint,…

Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

A: Solution: Given, Circle having center at (0, 0) and radius is 5 and

Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

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Q: Determine the moments of inertia of the Z-section about its centroidal xo- and yo-axes. -130 mm 21…

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Q: Write down a parametrization r(u, v) for the portion of the plane x - y+ z = 3 that lies inside the…

A: r(u, v) = ( u cos v , u sin v,  3 - u cos v + u sin v)  Where u € [0, 1]           v€ [ 0,2π]

Q: Find a formula for the distance from the point P(x, y, z) to thea. xy-plane. b. yz-plane. c.…

A: Distance FormulaDistance between two points x1,y1,z1 and x2,y2,z2d=x2−x12+y2−y12+z2−z12

Q: 2. At what point on z = a? + y? is the tangent plane parallel to 3.r – 4y + z = 7 ?

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Q: (a) Find equation of the tangent plane and normal line to the sphere x + y +z = 25 at the point…

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Find the points on the surface 2a2+ ly? + 522 = 1 at which the tangent plane is parallel to the…

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Q: A point moves along the intersection of the elliptic paraboloid z = 6r + 7y and the plane y = 2. At…

A: Given: A point moves along the intersection of the elliptic paraboloid z = 6x2 + 7y2 and the plane y…

Q: : The curve C is intersecting by 12r² +9y? = 36 cylinder and - V3r plane from the point (0, 2,0) to…

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Q: A point moves along the intersection of the elliptic paraboloid z = 2x? + 7y² and the planex = 4. At…

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Q: Suppose you head toward the xy-plane from the surface x? + y? – 2² = –1 at the point (1, 1, v3) by…

A: given,     x2+y2-z2=-1 at the point 1,1,3

Q: Find rectifying plane of et, é, t at the curve t%3DL

A: Given curve is αt=et,e-t,2t.  To find the rectifying plane of the curve . Result: Let rt→=xt,yt,zt…

Q: Find a parametrization of the line through the origin whose projection on the xy-plane is a line of…

A: To find the parametrization of line

Q: Find a parametrization for the curve described below. the line segment with endpoints (4,1) and…

A: The line segments between  (xo , yo)  and  ( x1, y1)  can be expressed as:x(t) = (1 − t)xo + tx1…

Q: Suppose the plane So thet its Coordinates are a partile Pir moving in given by y=Fsinzt Plxy) where…

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Q: Find a parametrization of the circle of radius 4 in the xy-plane, centered at the origin, oriented…

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Q: Determine the orthogonal trajectories of the family of circles (equation below) that is tangent to…

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Q: %3D the tangent plane at the point with ry coordinates (x, Y) = (0, 1).

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: a. Find the equation of osculating plane to Z1 at t=0

A: A(0) = &lt; -2, 5, 4&gt;     ---(1)  B(t) = &lt; 3/5 cos t , 3/5 sin t , 4/5 &gt;    =&gt; B(0)  =…

Q: Find the equation of the tangent plane to the given surface at the point (0,-1,2). y = 2x2 – 2 - O y…

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Q: Find the parametrization for the curve  the lower half of the curve x+3=y^2

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Q: Parametrize the intersection of the surfaces using t = z as the parameter. (If there are multiple…

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Q: Find the natural parametrization of r(t) = 1²0₂ + 20y. What is this curve?

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Q: Find a parametrization for the line segment joining points (0, 2) and (4, 0) using the angle 0 in…

A: Given: The line segment joining (0, 2) and (4, 0). Do the construction as in below figure