6- 12 -8 2 4 P.

Q: Let us take the following rotation matrix: R = Cos 0 sin CON). sin 0 cos 0

A: Given       R=cosθ-sinθsinθ   cosθ

Q: Give a vector parametric equation for the line through the point (3, 1) that is perpendicular to the…

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Q: Sketch the polar curve r= Jcos 20 and r = 2cos0. %3D

A: To sketch the polar curve r = cos 2θ   and r = 2cos θ

Q: A passive rotation by an angle of a vector v in the xy-plane, measured counterclockwise in the…

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Q: Find the image of the vector (1, 1, 1) for the given rotation. 60° about the z-axis

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Q: Find the equation of the plane perpendicular to the curve r(t) = (sin(2t), t, cos(2t)) at the point…

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Q: Find the parametric equation of the line that passes through point P(2,3,4) and is perpendicular to…

A: To Determine: Find the parametric equation of the line that passes through point P(2,3,4) and is…

Q: In math land, there is a clock. The hour hand of this clock is 1 ft long. However, the clock is…

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Q: (3) Find a parametric equation for the line segment joining (1, 0, 1) and (0, –2, 1).

A: The direction vector of the segment is: (0,-2,1) - (1,0,1) = (-1, -2, 0) Initial point is (1,0,1).…

Q: Transform (4, 7/3, ) from spherical into cylindrical form (here o is any angle).

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Q: Prove that a rotation of θ, where cot 2θ = (a − c)/b, will eliminate the xy-term from the…

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Q: Find a parametric equation for the line through the point(1,9,3) and perpendicular to the plwne…

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Q: V3y] |V3x + y] Show that T is a rotation through an angle 6, then compute 0.

A: Given the transformation is Txy=12x-3y3x+y. Find the angle θ.

Q: (Picture of question is attached)

A: Calculate the values using the given polar equation and complete the table.

Q: the xy-plane, centered at the origin, oriented clockwise so that the point (5,0) corresponds to t =…

A: we have to find parametrization of circle.

Q: Graph the line and conic section. r = 1/(1 + 2 cos u)

A: To graph r  = 11 + 2 cos u.

Q: 6. Find the image equation of the line -2x + y + 3 = 0 under the rotation about C = (1, 1) at an…

A: The resulting image is perpendicular to the given line.

Q: 7) What will be the coordinates of K' after a +90 degree rotation about the origin? Use parentheses.…

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Q: Y=V Cos 2O

A: The given function is, rθ=cos2θ The interval of θ is 0, π4 The axis of rotation is y-axis To find…

Q: Plot the points with polar coordinates 4, and 3, using the pencil. 4 2n 3 4 0. 4. 9. 11n 9. 5T 4 4…

A: Topic:- Geometry

Q: 2. Let r>o and Fo tina20 And use polar coordinates KZQ and use polar coordiinates (8,7) >(0,0)

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Q: Consider the curves:r = 4sin 0 and r = 2 sin(0) + 2cos (0).

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Q: Find the angle between the plane z=0 and the plane passing through the points (0, 0, 0), (3, 1, 0),…

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Q: Graph the curve r2 = 4 cos θ in the Cartesian xy-plane

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Q: Transform to spherical coordinates: F 102-8ỹ+6ż at point P (10, 8, 6)

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Q: What is the minimum angle of rotation (in degrees) that will carry the six-sided star onto itself: I…

A: It is a 6 sided star that means it will redivided into 3 parts:⇒ we divide 360°( full rotation ) by…

Q: In math land, there is a clock. The hour hand of this clock is 1 ft long. However, the clock is…

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Q: Show that every vertical line in the xy-plane has a polar equation of the form r = a sec u.

A: The relation between polar coordinates r,u and rectangular coordinates x,y is x=rcosu…

Q: The notation (x, y) --> (x, y) defines a rotation on the coordinate plane. O True False

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Q: Find the image of (2, –2) after a counterclockwise (passive) rotation of the axes about the origin…

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Q: Sketch a graph of the helix r(t) = (- cos(2πt), 4 sin(2πt), 3t), listing the rotation direction,…

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Q: Find parametric equations of the line through (–3, 0, 3) that is parallel to 5i – 8j+ k. x(t) y(t)…

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Q: Which of the following is the spherical coordinates of the point (0, v3, 1) which is given by…

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Q: Show that every vertical line in the xy-plane has a polar equation of the form r = a sec θ

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Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t 2 0. Find an equation for the projection of…

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Q: Parametrize the directed line parabolic segment y = x2 that joins 2 + 4i to −1 + i.

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Q: the Image tion of theT line 2x ty -1=0 under the rotation about wんat is equati the point (i,!) angle…

A: What is the image equation of the line 2x+y-1=0 under the rotation about the point (1,1) at an angle…

Q: Find a parametric description r(t) for the ine segment from (-1,-3,-1) to (1,7,4). Provide your…

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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: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

A: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

Q: Consider the curve. (금) 2 = 1 19 + Identify all possible parametric equations for the given curve. O…

A: In this question, we can check one by one parametric equation in the given curve.

Q: What solid of rotation is created here if the axis of rotation is the x-axis? -2

A: to find:- type of solid generated after rotation about the x-axis.

Q: find the volu me of the o bócct Caused by the rotation oftne bouncled ared be twen y= aQ ,y=X…

A: Integrals and derivatives are considered as the inverses of each other. For example if we have a…

Q: Which of the following is the cylindrical coordinates of (-1, -/3,2)?

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Q: 6. Find the image equation of the line –2x + y + 3 = 0 under the rotation about C = (1, 1) at an…

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Q: Convert the point from cylindrical coordinates to spherical co (3,2,0) (p, 0, 4) = || X

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Q: Integrate counterclockwise dz by Cauchy's formula 9. - 3 counterclockwise around the circle C : |z –…

A: Given that integrate counterclockwise  ∮Cz2z2-9dz by Cauchy's formula where  C : |z-3-3i|=32π.…

Q: 6. Find the projection of u = -7 onto the -2 line e of R given by the parametric equation l = tũ, -1…

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