Let l be the line y = - (7x + 5) in R21 Find vectors dland b so that v = a + tblis a parametric equation for L. +1

Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

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Q: Find a parametrization of the line passing through (2, 0, 4) and (4, 1, 2). r(t) =

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Q: The vector equation for the curve of intersection of the surfaces a = y? and z = y in terms of the…

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Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (4, –6) + t(1,…

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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: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² – 2x + 2y…

A: The given equation is: 2x2+2y2-2x+2y=7...(1)

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: The length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the…

A: Given information: Parametric equation of curve is : x=x(t)y=y(t)z=z(t) We need to find the length…

Q: What is the vector parametric equation L(t) for the line through the points (5,-5,0) and (0,-3,3)?

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Q: Which of these is the correct parametrization of the line connecting (1,2,5) and (0,3,- 1)? A. x =…

A: A line connecting the points x1,y1,z1 and x2,y2,z2 can be calculated as,…

Q: Express the given parametric equations of a line using bracket notation and also using i, j, k…

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Q: Sketch the curve parametrized by r(f) = (1 – 12, 1) for -1sı<1. Compute the tangent vector at i = 1…

A: Let's first draw the curve -  Domain - -1 ≤ t ≤ 1 where, we can take values of t as -  t = -1, -0.5,…

Q: Find parametric equations for the line through the origin parallel to the vector 3j + 9k. Let z =…

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Q: Find a vector parametrization 7 (t) for the intersection between the two surfaces: x² + 10y4 + 223 =…

A: According to the given information, it is required to find a vector parametrization for the…

Q: At which point P does the curve r(t) = ( 21°, 21°, 3t – 1) given in vector form have the tangent…

A: Given r→(t) = 2t3 , 2t2 , 3t-1 Then r→'(t) = 6t2 , 4t , 3 Tangent vector at a point is given as 24 ,…

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

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Q: Two plane curves are defined by the vector functions r1 (t) = (t, 2t – 4) and r2 (u) = (2u, u²).…

A: r1t=t,2t-4 and r2u=2u,u2 For the intersection point, t=2u   ...1u=t22t-4=u2    ...2 Convert the…

Q: Assume that the cylinder in Figure has equation x² + y² = r² and the plane has equation z = ax + by.…

A: To find the vector parametrization r(t) of the curve of intersection using the trigonometric…

Q: Consider the vector function      r(t) =〈t^2 - t, t^2 + t, t^3〉 Find equation of three different…

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Q: The vector equation for the curve of intersection of the surfaces x = y² and z = y in terms of the…

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Q: Find the vector r' (to); then sketch the graph of r (t) in 2-space and draw the tangent vector r'…

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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: At which point P does the curve r(t) = ( 2t2, 4t +1, t³ ) given in vector form have the tangent…

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Q: Give the length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in…

A: given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the vector form.

Q: Find the vector parametric equation of the line that passes through the points P(6,–2, –1) and…

A: The vector equation of a line is  . Where represent the position vector,  represent the direction…

Q: Let S be the plane defined by 5x-Sy+10z 0, and let T be the plane defined by 2x-2y+5z=-2. Find the…

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Q: Represent each of the following equations in R2 by a vector-valued/parametric equations: 1. y = mx+…

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Q: Consider the line perpendicular to the surface z=x^2+y^2 at the point where x=3 and y=2. Find a…

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Q: Give the two unit vectors u such that the function z = g(x, y) of example 3 has zero derivatives at…

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Q: Find a parametric form for the line through the point (0, –7, -9) and parallel to the vector 6i – 7j…

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Q: Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).

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Q: Find the parametric equations of the tangent line to the curve represented by the vector function 7…

A: Topic  = Vector

Q: Find the parametric equation for the line where the planes 7x – 6y + z = 10 and 2x + y – 3z = 4…

A: We have, r(t) = (0, -2, -2) + t(17, 23, 19) The detailed solution is as follows below:

Q: Choose the normal vector of the tangent plane to the surface defined by z =e4x²+16xy-9y2 at the…

A: Explanation of the answer is as follows

Q: Compute the unit binormal vector and torsion of the curve r(t) = (8t, 5 cost, 5 sint (5, 8 sint, -8…

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Q: Write an equation of the tangent plane to the parametric surface: r(u, v) = (u + v)i + 3u^2j + (u −…

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Q: Give a set of parametric equations for the line L4 that lies tangent to the graph of the vector…

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Q: Find parametric equations for the line whose vector equation is (a) (x, y) = (3, –5) + t(1, –2) X =…

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Q: Complete the parametric equations for the line wherekche planes 2=0and-2z + 2y + 2z -4 intersect.…

A: The equation of the planes are: P1: 2z = 0 ⇒ z = 0                                  .........1 P2:…

Q: Find a vector parametric equation for the ellipse that lies on the plane z (x + 2 - cylinder x + y =…

A: Dear student. You have posted many parts, according to the policy we will answering the first part.…

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

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Q: The planes 5x+ 2y + 2z = 5 and 3x + 5y = -22 are not parallel, so they must intersect along a line…

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Q: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² − 2x + 2y…

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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: Express the given parametric equations of a line using bracket notation and also using i. j.k…

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Q: At which point P does the curve r(t) = ( 21, 4t +1, t) given in vector form have the tangent vector…

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Q: G. Find the parametric equations of the line tangent to the curve C defined by the vector equation…

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Q: Suppose F(x, y) = x?i+ y?j and C is the line segment segment from point P = (-5, –5) to Q = (-3,…

A: Given data: The given expression for the vector is F→(x,y)=x2i→+y2j→. The given first point is…