Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter z = x² + y², z = 81 x = 9 cos(8nt)

Q: Find the vector and parametric equations for the line through the point P(4, -2, -4) and parallel to…

A: Find the vector and parametric equations for the linethrough the point P4,-2,4 and parallel to the…

Q: Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point…

A: We will find shadow of given points on the plane given and then find parametric equation of the line…

Q: Find a parametrization of the line in which the planes x- 2y - 2z = 3 and -3x + 3y + 3z = -6…

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Q: let angle thetha be measured from x1 axis counterclockwise to a line drawn normal to the boundary…

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Q: he vector v = , is tangent to the surface x2 + 2y3 - 3z2 = 3 at the point (2, 1, 1).  Find a.

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Q: Find a vector function that represents the curve of intersection between the paraboloid 2 z = 4x² +…

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Q: Give a vector parametric equation for the line that passes through the point (3, 5, –5), parallel to…

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Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

A: To find the equation of line with parameter t of the intersection of the planes  x + y + z =4 and…

Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

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

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Q: Find a parametric representation for the surface. the plane that passes through the point (0, -1, 5)…

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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: Let l be the line y = - (7x + 5) in R21 Find vectors dland b so that v = a + tblis a parametric…

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Q: Calculate the velocity and acceleration vectors, and speed for when t = Speed: 11. Velocity:…

A: To calculate the velocity and acceleration vectors, and speed for .

Q: Vector F is mathematically defined as F = M x N, where M = p 2p² cos + 2p2 sind while N is a vector…

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