Write the line through p = (3, 2, 2) in the direction of v = (-1, –4, 2) in vector parametric form: L(t) =

Q: Find the vector form of the equation of the line inR3 that passes through P = ( -1, 0, 3) and is…

A: Equation of a line passes through  x1, y1, z1 having direction ratios a, b, c is, x-x1a=y-y1b=z-z1c

Q: Sketch the graph of the plane curve r(t) = (2t + 1)i − t2j and sketch the vectors T(t) and N(t) at…

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Q: Find a vector parametrization of the line through P = (3, –8, 5) in the direction v = (-2, 0, 3)…

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Q: H=pz Csup ap te'sin dg tpan 2 At point (1, ,6)

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Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x= 2+3t y…

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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: 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: Write the line through p=(5,2,2) in the direction of v¯=⟨3,5,0⟩ in vector parametric form: L(t) =…

A: We know that the equation of line passing through the point P in the direction of v→ is…

Q: Given the points A(2,6,0) and B(3,5,6) determine the equation of a line vector in parametrix form

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Q: The jet stream is blowing at 60 miles per hour in the direction N45°E. Express its velocity as a…

A: The jet stream is blowing at 60 miles per hour in the direction N45°E We need to express its…

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

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Q: Show that the vector v = [a, b, c]* is perpendicular to the plane P with equation ax + by + cz + d =…

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Q: The curve with vector equation r(t) = t'i + 2tj+ 3tk is %3D a line.

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

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Q: Express the equations of the lines r · (i −j) + 7 = 0,r · (i + 3j) − 5 = 0 in parametric forms and…

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given vectors area. u=2,0,2w=-2,-1,0a=0,0,0 Find the vector equation of the line perpendicular to u…

Q: Let L be the line defined by the vector equation v = [ -1, -3 ] + t [ 1, -2 ]. Find the equation y =…

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Q: 1 - Find a vector equation and parametric equations for the line segment connecting P(a, b, c) and…

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

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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: the vectors y₁, y₂, Y3 (where y; E R² V i) must be linearly dependent?

A: Given the vectors y1, y2 and y3 in the vector space R3.

Q: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

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Q: Find an equation of the plane that contains the point (-1, 2, 3) and is perpendicular to the line…

A: The plane is perpendicular to the line, then the direction vector of the line is normal to the…

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

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Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

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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 parametric equations for the line whose vector equation is given. (a) (x, y) = (2, –5) + t(1,…

A: Parametric equation of the line, <x,y,z>=<a,b,c>+t<p,q,r> , t is a scalar is given…

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: 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: A velocity vector of v = 3t2i − 6t3 j − 4K ft/s  is governing the movement of an object in the 3D…

A: It is given that v=3t2i-6t3j-4kfts. Also, object starts at -1,4,5 at t=0. That is, s0=-i+4j+5k.…

Q: 1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point…

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

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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: Sketch the curve whose vector equation is r(t) =

A: given rt=<tcost,tsin,t>

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 2x² + y²…

A: Given: Let us take x = t. So, we get y=t4  and  z=2t2+t42=2t2+t8.

Q: Given a the vector equation r(t) (4 + 4t)i + (1 + 1t)j + (1 + 4t)k, rewrite this in terms of the…

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x2 + y?…

A: z = 4x2 + y2  ,  y = ex    We observe that the given two equations, here we can see that y can be be…

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

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x2 + y and…

A: The given curves are: z=4x2+y2     and     x=ey

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

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Q: The velocity of a particle is given in terms of the time t by v = sinti - 2cos(2t)j + t2k   where…

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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 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…