Part a) Find a parametrization for the line passing through the two points (7, 8, 6) and (8, 8, – 6) Part b) Find a parametrization for the line SEGMENT from (7, 8, 6) to (8, 8, – 6).

Q: Convert the point from cylindrical coordinates to rectangular coordinates. (9, T, 8) (x, у, 2) %3D

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Q: Develop vector and parametric equations for the line through (7,2,-1) and parallel to r = (4,7,0) +…

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Q: The unit vector of the PQ (of point P(-3, 4, 1) and terminal point Q(-5, 2, 2)). - The angle between…

A: here we have

Q: Find parametric equations for the line described below. The line through the point P(-3, -4, -2)…

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Q: Find a set of parametric equation of the line through the point (-2, 0, 3) parallel to the vector v…

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Q: Find a set of parametric equations of the line with the given characteristics. The line passes…

A: Given: Point (2, 3, 4) and plane 3x + 2y − z = 6. To Find: Equation of the line passing through the…

Q: ear equation of the plane through the nts (6, 3, 2) and (4, −1, 1).

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Q: 1. Give parametrizations of each curve. a. The line through (-2, 5) and (5, - 1) such as i goes from…

A: The difference between the x values= 5-(-2)=7  The difference between the y values= -1-5=-6  The…

Q: 33) Given point P(1,2, 3) and vector n= î + ĵ , find point Q on the x-axis such that PQ and în are…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: a) Write parametric equations for the plane in Rº that passes through the point (2, 3, 1) and is…

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: Points A and B are known to lie in a plane. a. What can you say about AB? b. State the postulate…

A: Solution: Consider the given that A and B are two points in any plane  (a) According to the…

Q: Consider A = (3, –1, 5), B = (1,3, 7) and C = (2, 2, 2). 20 Find a parametrization or equation(s) of…

A: The direction ratio of the line is B-A=(1,3,7) - (3,-1,5)=(-2,4,2)

Q: and the plane - 3 X + Z Intersect along a line. Find Parametnic desenetion of this la

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Q: Q1: Find the parametric rquations of the line that passes through the point P(4,2,-3) and Q(-3,2,2).…

A: Here we have to find the parametric equation of the line that passes through the point P(4,2,-3) and…

Q: Prove that the centroid of a parallelogram is the point of intersection of the diagonals of the…

A: The vertices of the parallelogram are (0, 0), (0, a), (b, c), and (b, a + c)

Q: 103. Show that the parametrization of the ellipse by the angle 0 is ab cos 0 X = a² sin² e + b² cos²…

A: From given data,

Q: (a) Find a vector parallel to the line of intersection of the planes 4x + 3y – 2z = -5 and -5x + y –…

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Q: Sketch the set (described in cylindrical coordinates). r = 4

A: GIVEN r=4 we need to sketch the cylindrical coordinates

Q: > A Moving to another question will save this response. uestion 3 Find a parametrization for the…

A: Given that: (3, -7, 4)and (0, -7, 7)   NOTE: As per our answering guidelines, we can only answer 1…

Q: The parametric equation of the segment [AB] with A(1,0,5) and B(3,1,2) is: O x=1+2t y%3Dt z-5-3t -o<…

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Q: A triangle has vertices A(1,3), B(7,0) and C(4,6). Determine the equation of Euler's line? Hint:…

A: Sketch the triangle:

Q: 5) Find the distance from D to the plane containing A, B, and C NOTE: Enter the exact answer.…

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Q: In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase.…

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Q: 3. Find an equation the plane curve about the inc

A: INTRODUCTION: In mathematics, functions are the most fundamental aspect of calculus. Functions are…

Q: Write down the parametric equetions |3D 4=6-t in cartesion Form

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Q: Convert the point from rectangular coordinates to cylindrical coordinates. 11. (0,5,1) 12.…

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Q: Find a parametrization of the line in which the planes x- 2y + 2z = - 1 and – 4x+ 3y – 3z = -1…

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Q: A line passes through the point (8, - 5,7), and is parallel to the vector 9i + 7j + 10k. Find the…

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Q: 2. In parametrizing lines connected by two points in 3-D plane, A. there is only one correct…

A: Introduction: Parametrization is crucial in analytical geometry in three dimensions. In addition to…

Q: Find a parametrization for the line perpendicular to (4,-1,1), parallel to the plane 4x+y-8z=1, and…

A: The parallel line through the point has the vector equation L = &lt; 1,0,5 &gt; + t &lt; a, b, c…

Q: Find parametric equations for the line through p (2,3,0) and perpen-dicular to the vectors u =(1,…

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Q: (s) (a) Find a parametric equation for the line through (2, 4, 6) that is perpendic- ular to the…

A: Equation of line in 3D

Q: Find a set of parametric equations and symmetric equations of the line ` con- taining the point P(1,…

A: Given Point is (1,-2,3) And Plan is : 2x-y+3z=6

Q: 5 Find a parametrization for the line segment joining the points (0, 2) and (4,0) using the angle in…

A: A parametrization for the line segment joining the points (0,2) and (4,0) using the angle θ in the…

Q: Convert the point from cylindrical coordinates to rectangular coordinates. 3, 4 2 (х, у, 2) 3D

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Q: a) Find the distance from a point (3,5,6) to a plane 2x + 3y + 5z = 1 b) Find the angle between the…

A: Find the distance of the point to the plane and find the angle between the given planes.

Q: Find parametric (or vector) and symmetric equations of the line which pass through the points P,…

A: P11, 4, 6 &amp; P22, -1, 3. Vector equation of a line passing through two points with position…

Q: Find a set of parametric equations for the line passing through the point (7, 0, 2) that is parallel…

A: We are asked to find the equation of the line.

Q: Find a parametrization of the line in which the planes x+ 4y + 2z = - 1 and 3x + 6y + 3z = 3…

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Q: Find a parametric represent at ion for the plane that passes through the point (2, -3, 4) and cont…

A: It is asked to find the parametric form of plane that contain vectors a = &lt; 5, -1, -2 &gt;    and…

Q: Find the equation for the plane through the point Po = (2,7,6) and normal to the vector n= 3i + 5j +…

A: Given:-normal, n=3i+5j+6kpoint on the plane, P0=2, 7, 6let (x, y , z) on the plane vector (x-2)i+…

Q: Find a vector parametrization for the line with the given description. Perpendicular to the…

A: Given points are (0,0,8). The equation of yz-plane is given by ⇒x=0 Therefore, the normal vector is…

Q: -. Which coordinate plane is closest to the point (7, 3, 8)? Find an equation of the sphere with…

A: we have to find the coordinate plane that is closest to the point 7,3,8 and also find the equation…

Q: 5. Find parametric equations for the line of intersection of the planes x + y = 1 and y +z = 1.

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Q: Flnd the parametric equation of the line of ntersection of the planes and

A: First find normal vector then take cross product and use formula

Q: 6. Find a parametric representation of the line of intersection of the two given planes. 2x+ y- z= 6…

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Q: 3. The position vector [3 2 1 1] lies in the YZ plane and forms 30 degree with the principal axis.…

A: Given: Position vector 3211 lies in the YZ plane and forms 30°. To find: On rotation, it forms 45°…

Q: Find the equation for the plane through the point Po = (8,4,8) and normal to the vector n=2i + 2j +…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.