Find the distance of the point (2, 6, –4) from the line r(t) = (-1 + 31, –1+41, 5 – 2t). Give a vector parametric equation for the line through the point (1, –4, 1) that is parallel to the line (4 + 5t, 1 – 4,3 + 5t): L(t) =

Q: Find the parametric equations for the line through the point of intersection of the lines L,:x = 2…

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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: Sketch the graph of the plane curve . r(t) = ti − t3j and sketch the vectorsT(t) and N(t) at the…

A: Here we are taking the T(t) as the tangent vector and N(t) as the Normal vector Consider the…

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

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Q: Consider the curve C parameterized by ã() = (P + 21 + 3, –2t – 4,2 – 1), - 1.4 Where, 1€ [0, +o0[.…

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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: find T, N, and B for the curve at the indicated point. Hint: After finding T', plug in the specific…

A: The unit tangent vector T, the unit normal vector N and the unit binormal vector B are three…

Q: Find the parametric equations for the lines. Where, the line through the point P (3, -4, -1)…

A: Topic = Vector

Q: a line is parallel to the vector 2i + 7j+ 8k and passes through the point P = (3,6, 6), then the…

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

A: Given, The parametric equation of the line D passing through A and parallel to vector v is  x =…

Q: Find a parametric equation for the line that passes through points A (3,-2,4) and B (5,6,-2). x = 3+…

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

A: Given, r(t)→=2t2,4t+1,t3  tangent vector 4,4,3 we know derivative of vector valued function gives…

Q: If a line is parallel to the vector 4i + 1j+ 4k and passes through the point P = (3,7,9), then the…

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Q: Consider the curve C parameterized by f(t)=(t^2+2t+3,-2t-4,t^2-1),t E [0,+infinite[ a)Find the plane…

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Q: Find the parametric equation for the line in R' that passes through the point (1, –2, 3) and that is…

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Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find a.…

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Q: Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface.…

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

A: Given, Line D = x = 2+3ty = -1-4tz = 2  It is passing through A and parallel to the vector v  We…

Q: Find the parametric equations for the line through the point of intersection of the lines L1:x = 2 +…

A: In line L1 and L2  't' is used as parameter but don't confuse with it. Different different line we…

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

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Q: Find a scalar equation for the plane that contains the points P, Q and R

A: We know that equation of plane passing through three points A(x1,y1,z1),B(x2,y2,z2), C(x3,y3,z3)  is…

Q: Find the angle between the two planes x- 2y + z = 29, 2x + 3y – 2z = 6. And also find the parametric…

A: here we will find angle between two planes and parametric equation of plane's line of intersection,

Q: Complete the parametric equations for the line where the planes 8x + 11y + 4z 13x + 2y + 3z = 5…

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

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: Find a parametric equation for the line through the point (2,3, – 1) and perpendicular to the plane…

A: Given that The point on the line (2,3,-1) and perpendicular to the plane 8x+3y+3z=5 A vector…

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

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Q: If a line is parallel to the vector 3i + 2j + 1k and passes through the point P = (1,3, 8), then the…

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Q: If a line is parallel to the vector 3i +2j+ 1k and passes through the point P = (1,3,8), then the…

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Q: Find a vector tangent to the curve of intersection of the two cyclinders ? + y² = 98 and y² + z² =…

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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: Let C be the curve of intersection of the surfaces with equations   x2 + y  =  5   and   24x + 4y…

A: Given: Let C be the curve of intersection of the surfaces with equations x2+y=5  and   24x + 4y + z…

Q: Complete the parametric equations for the line where the planes 8x + 13y – z = 27 and 9x + 15y – 12z…

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Q: Consider the line l in R³ given by the parametric vector equation 3 1 -2 -1 and the plane described…

A: Given that the line l in R3 given by the parametric vector equation and the plane described by the…

Q: Compute the parametric equations of the line in R3 determined by the intersection of the two planes:…

A: To obtain the parametric equations of the intersection line, use the following formulae. Let n1→…

Q: If a line is parallel to the vector li + lj+ 4k and passes through the point P = (8, 4, 8), then the…

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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: Find a vector equation for the line through the point P = (4, -2, -4) and parallel to the vector vv…

A: P= (4,-2,-4) is a point on the line.  And the line is parallel to v=(4,-1,4)  v is the velocity…

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

A: Let's find.

Q: Find the position vector for the particle with acceleration, initial velocity, and initial postion…

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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: 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 a vector equation and parametric equations in t for the line through the point and parallel to…

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Q: Find the parametric equations for the line of the intersection L of the two planes. 6x – 3y+ z = 5…

A: Parametric equations of the line is :  x(t) = x0 + a t  y(t) = y0 + b t  z(t) = z0 + c t  Here ( x0…

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…

Q: (a) Find a vector parametric equation for the ellipse that lies on the plane 3x + 2y + z = -4 and…

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