b) Find the area of the triangle with vertices P, Q, R. c)Write down parametric equations for the line normal to the plane and passing through P

Q: Find parametric equations for the line through (-2,0,4) parallel to V=2i +4j -2k .

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Q: Explain why in spherical coordinates the graph of = c is a half-plane and not an entire plane.

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Q: In the given equation as  follws , find a set of parametric equations forthe rectangular equation…

A: Given :                 y = 2x -5 , t=0 at point (3,1)

Q: Complete the parametric equations for the line where the planes – 3x – 9y – 12z - 11x + 2y – 10z 33…

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Q: Find a set of parametric equations for the rectangular equation that satisfies the given condition.…

A: Given :                y = 2 x - 5  ,  t = 0        at point (3,1)

Q: Graph the surface whose spherical equation is p = 1– sino.

A: We use maple software to graph the given surface.

Q: Find parametric equations of the line through (-3,0, 3) that is parallel to 5i– 7j+k.

A: Recall:  The parametric equations of the line through (x0,y0,z0) that is parallel to a i+b j+c k is…

Q: Find parametric equations for the line segment joining the points (5, 3) and (11, 11). x=t, y = 3 +…

A: Solution

Q: Sketch the set of points that are described in spherical coordinates where: TT pS 2, 0<0<2' 2 くp<T

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Q: osen y

A: Is it sen y =x

Q: Eliminate the parameter to write the parametric equations as a Cartesian equation. If x(t) = 3t – 2,…

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Q: In each part, find an equation of the sphere with center (5, –8, –2) and satisfying the given…

A: Given  Centre of sphere is =(5,-8,-2)

Q: Convert the following quadric surface into spherical coordinates.

A: Convert the quadric surface into spherical coordinates.

Q: Sketch the plane curve represented by the parametric equations x = Vi and y = 2t – 1 by eliminating…

A: Sketch the plane curve represented by the parametric equations             x=t     and     y=2t-1 by…

Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: a +…

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Q: In each part, find an equation of the sphere with center (2, –3, –3) and satisfying the given…

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Q: Consider two non-parallel lines , l1 & l2, in R³ with parametric equations l1: P+ tu l2: Q + tv.…

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Q: The spherical coordinates of a point P are given by (2,). The rectangular coordinates of the point P…

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Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

A: Here we have to find the parametric equations of the curve C of intersection of the cylinder S:x2+y2…

Q: Which of the following shapes could tessellate a plane on their own?

A: We know that triangles, squares and hexagons are the only regular shapes which tessellate by…

Q: Use parametric equations to derive the formula for the surface area of a sphere of radius a.

A: We know that parametric equations of the sphere, x=acosθsinϕy=asinθsinϕz=acosϕ So parametric vector…

Q: Find parametric equations for the line through (-2, 0, 4) parallel to v = 2i + 4j - 2k

A: we know that parametric equation of line which passes through point x0,y0,z0 and parallel to vector…

Q: Consider three points in three-dimensional space: A = (15, 2, –3), B = (2, –3, 15), C =(-3, 15, 2)…

A: The parametric equation of a line passing through the point and in the direction of  is defined by…

Q: Find the rectangular coordinates of the point whose spherical coordinates are given. (a) (3, 0, 0)…

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Q: d) Find the parametric equations for the line of intersection of the two planes.

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Q: The angle and the parametric equations for the intersect line between planes a + y = 1, and 2r+y-2z…

A: Given, x+y=1, 2x+y-2z=2 we know angle between two plane is…

Q: Show that the graph of the parametric equations x = a + (c − a)t, y = b+(d−b)t, t ∈ [0, 1] is a line…

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Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: æ? +…

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Q: Find parametric equations, in terms of t, of the line passing through (2, 2, 12) and parallel to the…

A: Given: The line is passing through 2,2,12. Also, it is parallel to the line: x=5-9ty=2z=4+t The…

Q: Consider the point (−6, 2, 2), line l : (1 − x)/7 = y − 3 = z/2. Find parametric equations of the…

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Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve),…

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Q: Find a set of parametric equations for the curve of intersection of the paraboloid r² + 4y² -z = 0…

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Q: What is the parametric equation for the line through the point (1,2,3) parallel to the y- axis? (a)…

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Q: Identify the surface whose equation in spherical coordinates is given by p = 2 cos o %D

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Q: Show that the parametric equations x a cosh u cos v, y b cosh u sin v c sinh u represent a…

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

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Q: Find parametric equations of the line through (-2, –1, 3) that is parallel to 2i – 3j+k. x(t) = %3D…

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Q: Find a parametric description for the top half of the unit circle, oriented clockwise.

A: Given that, the top half of the unit circle is considered. The standard equation of a unit circle…

Q: Please help me with this problem

A: Parametric equation:

Q: What is the rectangular equivalence to the parametric equations? x(θ)=2sinθ+1,y(θ)=3cosθ−2 , where…

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Q: Find the rectangular coordinates of the point, whose cylindrical coordinates are given. (а) (3, п,…

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Q: Find the rectangular coordinates of the point (G) which is in spherical coordinates.

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Q: Find the angle of intersection of the plane -2x – 3y – 5z = -4 with the plane 5x + 5y + 4z = -5.…

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Q: The angle and the parametric equations for the intersect line between planes a+y = 1, and 2r +y - 2z…

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Q: Find the distance between the point (4, −1, 5) and the line given by the set of parametric equations…

A: The point is: P(4, −1, 5) The line is: x = 3, y = 1 + 3t, z = 1 + t The line is: &lt;3, 1, 1&gt; +…

Q: The angle and the parametric equations for the intersect line between planes x + y = 1, and 2x + y–…

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Q: Give two parametric representations for the plane curve. 1. y#-4 y + 64 %3D

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Q: What is the Cartesian form of the parametric equations æ(t) = 4cost – 1 and y(t) = 5sint + 2?…

A: Here I am attaching image so that you understand each and every step.