Find the vector equation that represents the curve of intersection of the paraboloid z 2x2 + y and the surface z = e". Write the equation so that one of the functions is simply t.

Q: Find a vector normal to the plane with the given equation.9x − 4y − 11z = 2

A: Our Aim is to find a vector normal to the plane with the equation given below:-9x-4y-11x=2 -(i)

Q: Find a vector normal to the plane with the given equation. 3(x – 5) – 5(y – 1) + 10z = 0 n =

A: Consider the equation of the plane passing through a general point Po and with normal vector n.

Q: Calculate the vectors A and C curves given below with aA dl

A: In this question, we have to calculate the line integral in both parts.

Q: Resolve the vector of 300N at N25W into its rectangular components. Use right/left and up/down for…

A: To resolve the vector

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: Find a vector n normal to the plane with the equation 5x - 5y – z = 10. n = (5,

A: Given equation of plane is 5x-5y-z=-10.want to find:Normal vector n to given plane.

Q: Find a unit vector n that is normal to the surface 4z? – 2x* – 3y = 14 at P = (1,2, 4) that points…

A: To Determine: Find the unit normal n that is normal to the surface at p(1,2,4) that points in the…

Q: Find a vector function that represents the cur ve of intersection of the paraboloid z a + mnd the…

A: Given that, the paraboloid is z=x2+y2 and the cylinder is x2+y2=22. The projection of the of the…

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: Find the equation for the plane through the point Po = (2,3,8) and normal to the vector n= 3i + 8j +…

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Q: Find a vector parametric equation for the ellipse that lies on the plane 5y−3x+z=9 and is inside the…

A: Given that: 5y-3x+z=9 Let x=u cos v, y=u sin v So z=9+3x-5y  =9+3u cos v-5u sin v

Q: Find the equation for the plane through the point Po = (3,4,3) and normal to the vector n=21 + 7j +…

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Q: Find the cartesian equation of the plane that is normal to the vector n = -3i – 4j+4k and includes…

A: n=-3i-4j+4k  and P(2,-7,5)

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

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Q: Find a vector normal to the plane with the given equation. 2x + 8y + 9z = 3 n =

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Q: Determine the vector equation that represents the curve of intersection between the cylinder 2¹² +…

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Q: Evaluate F - dS, where F = and S is the helicoid with vector equation r(и, о) - = 0 < u < 2, 0 < v…

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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 a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: The intersecting curve of two surfaces is given as follows:

Q: Represent the plane curve by a vector-valued function. 2x − 3y + 5 = 0

A: Given: 2x-3y+5=0 for finding given equation in vector form, we assume x=t and find value of y in…

Q: Find a vector normal to the plane -2x - 3y = 12 - 4z.

A: Given  a vector -2x-y=12-4z. We need to find the vector normal to the plane.

Q: Find a vector normal to the plane with the given equation.3(x − 4) − 8(y − 1) + 11z = 0

A: Consider the equation of the plane: 3x-4-8y-1+11z=0.   If equation of the plane has the form:…

Q: The planes 5x+y+z=−6 and 3y+5z=22 are not parallel, so they must intersect along a line that is…

A: Given planes are 5x+y+z=-6 and 3y+5z=22 find the vector parametric equation

Q: Find the equation of the plane that passes through the point P(1, 0, 2) and contains the line whose…

A: Hi there, At a time we can answer only one question. So, I have answered first one (#6).

Q: Represent the plane curve by a vector-valued function. x2 + y2 = 25

A: It is given that, x2 + y2 = 25. Let x=5cost and y=sint , Then 5cost2+5sint2=25cos2t+sin2t=25

Q: Find a vector function that represents the curves of intersection of the two surfaces. 1.- The…

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Q: The unit normal vector to the surface x'y + 2xz? = 8 at the point %3D (1,0, 2) is

A:

Q: Find a vector parallel to the plane 2x - y - z = 4 and orthogonal to i + j + k

A: Given:A plane 2x - y - z = 4 orthogonal to i + j + k

Q: find The unit Vectors tangent and normal toThe ellipse x+ 2y=6 6at The Point (2,1).

A: I am going to solve the give problem by using some simple geometry to get the reuired result.

Q: Find a vector parametrization of line through P = (9, 8, 3) in the direction v = (4, -8, 6). %3D…

A:

Q: find The unit Vectors tanent and normal to The ellipse x+2y= 6 at The Point (2,1).

A: Given, ellipse x^2+2y^2=6   point=(2,1)

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: The unit vector normal to the plane 2x + 3y + 6z = 7 is

A: The given plane is 2x + 3y + 6z=7. The unit normal vector to fx,y is defined as n=∇F∇F. The normal…

Q: Find the second and the third components of a vector n normal to the plane with the equation 7x +…

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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: Sketch the curve of intersection of the surfaces, and find a vector equation for the curve in terms…

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Q: Find a vector n normal to the plane with the equation x+6y + 4z = -10. n= 00> (1₂)

A: Concept: The equation of the plane is written as: ax-x0+b(y-y0)+c(z-z0)=0 or ax+by+cz=d Here the…

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: Sketch the curve of intersection of the surfaces, and find a vector equation for the curve in terms…

A: First, we will sketch the curve of the intersection of the surface. The equation of the surfaces are…

Q: What is the perpendicular vector to the surface f(x.y.a)-ay-3r+'y-0 at (1,-1,2)? (3,3.0) (1,1.3)…

A: A vector that makes an angle of 90 degrees with the given surface is said to be perpendicular to the…

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

A:

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: Sketch the curve with the vector equation 7(t) = (t,2 – t, 2t). Indicate with an arrow the direction…

A: Solution

Q: Find the equation of the plane passing through the point (2,−1, 3) and normal to the vector N = (2,…

A: we know that equation of plane which passes through point x1,y1,z1 and normal to vector a,b,c is…

Q: Find a nonzero vector normal to the plane z−3(x−4) = −4(1−y) correctly.

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Q: Evaluate /1+ x² + y²dS, where S is the helicoid with vector equation т(и, 0) - = 0 < u < 3, 0 < v <…

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Q: Give a vector description of the midpoint M of a line segment AB→.

A: GivenLine segment AB→To find vector description of midpoint of AB

Q: Calculate the curvature of the vector function when t= -7: 7(t) = (1+ 2t, 7 – 3t, -8 + 5t)

A: