1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point (ro, yo) normal to the vector N (A, B).

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 + y2 = 50 and y? + 22 =…

A: Find a vector tangent to the curve of intersection of the two cylinderx2+y2=50 and y2+z2=50 at the…

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 the point on the graph of z = 3x2 + 2y at which vector (24, 8, 2) is normal to the tangent…

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Q: find a vector normal to the plane with the given equation. x − z = 0

A: Given: Plane: x-z=0 To Find: A vector normal to the given plane

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: Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and…

A: Given the curve y=10+4x-x2 at (x,y)=(3,13).

Q: Find a vector function that represents the curve of intersection of the paraboloid z = 7(x^2) +…

A: We have to find vector function that represents the curve of intersection of the paraboloid z =…

Q: Is the line x = 6- 3t, y = 8 + 8t, z= -t parallel to the plane 3x + y -z=2? Give reasons for your…

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Q: In Exercises 31-36, find a parametrization of the tangent line at the point indicated. t,4t 2,2t 3),…

A: Differentiation: The line must pass through the point at t=-2 is  (t,4t+2,2t+3)=(-2,-6,-1)

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 the vector equation of the plane tangent to the surface z = x^3 - y^3 at the point (0,1,-1)

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Q: Find the vector equation of the line of intersection of the planes x+y+z=1 and x+2y+2z=1.

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Q: 3. Find a vector function that represents the curve of intersection of the paraboloid z =. and the…

A: To find the vector function that represents the curve of intersection of the paraboloid z=x2+y2, and…

Q: Find a vector n normal to the plane with the equation – (x + y+ 52) = –4. n = (-1,

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Q: Consider the following lines: 4:z=1,y-1=-4,2=1-3t :z=2s+1,y=1-3s,z=1 y+1 z-1 2a Find the…

A: Explanation of the answer is as follows

Q: 1. Find a vector which is tangent to the curve of intersection of the surfaces z = x2 – y? and xyz +…

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Q: Find a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.

A: Introduction: We can determine the vector equation of the curve formed by the intersection of two…

Q: In Exercises 31-36, find a parametrization of the tangent line at the point indicated. ( 1 - t 2 , 5…

A: Given: The line given is r(t)=1-t2,5t,2t3. Substitute 2 for t in r(t)=1-t2,5t,2t3.…

Q: Find a vector normal to the surface 3z 3 + x 2 y - y 2 x = 1 at P =(1,-1,1) .

A: Given: 3z3+x2y-y2x=1 at P(1,-1,1)

Q: Find the point on the graph of z = 3x2 + y at which vector n = (24, 2, –1) is normal to the tangent…

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Q: a)What is the slope of the tangent line to the curve y=2sin4x  at x=⊼(pie)/4? b) Find a unit vector…

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Q: It is known that the acceleration vector for a particle is given by A(t) = 4j + 2tk. Determine the…

A: We need to determine vector equation of curve traced.

Q: 3. Write the scalar equation for a plane passing through (5,8,-1) and perpendicular to the line x =…

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Q: Suppose that the plane tangent to z = f(x,y) at (-2,3,4) has equation 4x + 2y + z = 2. Estimate…

A: As the given plane tangent to z=f(x,y) at (-2,3,4) is  4x+2y+z=2, that is z=2-4x-2y thus the…

Q: Which of the following vector functions represents the curve of intersection of the cylinder x2 +y =…

A: Given Data: The equation of the curve is: x2+y2=4 ......1 The equation of the plane is: x+z=3…

Q: Find equations of the normal line and the tangent plane to the parametric surface defined by the…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  compare coordinate on…

Q: Find a vector tangent to the curve of intersection of the two cyclinders x² + y? = 2 and y? + z² = 2…

A: To find a vector tangent to the curve of intersection of two cylinders        x2+y2=2 and…

Q: Show that the condition that the curves ..(1) ..(ii) ax? + by =1 %3D a'x² + b'y² = 1 1 1 1 Should…

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Q: Find the vector equation for the line of intersection of the planes 5x + 4y + 5z = 1 and 5z + z = -4…

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Q: Find a vector function that represents the curve of intersection of the paraboloid z=7x^2+5y^2 and…

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x² + y²…

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Q: At which point P of the curve defined vectorially with r (t) = (21, 4t + 1, t) is the tangent vector…

A: The general form of the parametric equation of the curve in three dimensional space is given by…

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: The position vector of a particle in the xy-plane is given by for all t > 0. The acceleration…

A: position vector of a particle in the xy-plane is given by < t^2+1, ln(2t+3) > for all t>=0

Q: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-2) in the…

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Q: Find a vector equation for the curve of intersection of the surfaces x^2 + y^2 = 4 and z = xy.

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

A: Let's find.

Q: Find the point on the graph of z = 3x2 + u? at which vector n (24, 2, –1) is normal to the tangent…

A: Gradient of the surface denote the normal direction.

Q: Find a vector function that represents the curve of intersection of the paraboloid z = x^2 + y^2 and…

A: Intersection of paraboloid and cylinder can be obtained by representing y in the form x and z in the…

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: Find a nonzero vector normal to the plane z − 5(x − 1) = −2(3 — y). - -

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Q: Show that A(x - x0) + B( y - y0) = 0 is an equation for the line in the xy-plane through the point…

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Q: Find the vector equation of the line of intersection of the planes x+y+z = 1 and x+2y + 2z = 1.

A: The equation of the line vector of the intersection of 2 planes can be calculated using the cross…

Q: The planes 3x−4y+5z=−28 and 4x−2y+4z=−24 are not parallel, so they must intersect along a line that…

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Q: Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and…

A: To find a vector function that represents the curve of intersection of the surface 4x+2y-8z2=16 and…

Q: Let ƒ(x,y) = x²e"9. Give the unit vector that points in the direction of maximum increase along the…

A: Given that: f(x,y)=x2exy& the point is (x,y)=(1,1)

Q: (b) Solve the electric flux through a paraboloid z = x² + y² – 16 that lies below plane %3D z = 0.…

A: As per our guidelines, we can only solve first question and rest can be reposted. The solution for…

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: Find the point on the graph of z = 3x2 – 3y? at which vector n = (48, –60, –2) is normal to the…

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