Find a parametrization for the line segment beginning at P, and ending at P2. P (2,-3,2) and P2(0, – 3, – 5) O A. x= 2t, y = - 3t, z = 7t - 5, 0 sts1 O B. x= 2t, y = - 3, z = 7t- 5, 0sts1 O C. x= - 2t + 2, y = - 3t, z= - 7t +2, 0sts1 O D. X= - 2t+2, y = - 3, z= - 7t + 2, 0sts1

Q: Find parametrizations for the lines in which the planes 5x - 2y = 11, 4y - 5z = -17

A: Given: The given two planes  5x-2y=11 and 4y-5z = -17 are intersects.

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A:

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t,…

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Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2, - 5) and…

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Q: Find the equation of the tangent plane to +y? at the point (2,-2,5) the surface z= 4 O r + 4y - % =…

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Q: findthe parametríc equatlons for the line through the paint of in tersecti of the lines 4=X=2+ 36 14…

A: first we find intersection point of given line

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

A: Solution

Q: Find the point in the plane x – 2y + z = 4 that is closest to the origin.

A: Solution)                   Given                           plane  x-2y+z =4

Q: Find the distance between the skew lines with parametric equations x 2 + t, y = 1 + 6t, z = 2t, and…

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Q: The following parametrizations intersect at the specified point. r1t) = (-5, 1, 2VF + 1), r,6) = (s,…

A: We have to look whether that point lies on both of the paths.

Q: Find equations for the planes The plane through P0(0, 2, -1) normal to n = 3i - 2j - k

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Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x) %3D and C is the curve in the third quadrant…

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Q: Find the plane thst passes through the equation of. the point P(6,0,-2) ¢ = 1+t, z=2 -t entains the…

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Q: Find parametric equations for the line segment joining the points (6, 2) and (9, 10). x=t, y 2+8t,…

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Q: Consider the following. C: line segment from (0, 0) to (4, 8) (a) Find a parametrization of the path…

A: Given:

Q: Find parametrizations for the line in which the planes 3r - 6y-2z = 3, and 2x+y-2z = 2 intersect.

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Q: Sketch the plane curve. r(t) = 2ti – tj, [0, 2] y y 2. 1 1 -1 1 4 -1 1 4 5 -1 y -1 2 3 4 1 2 3 4 5…

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Q: Q2/ Find the Parametric aned standand equatior of the line Hhat passer through Points (-2,1,0)…

A: The equation of line passing through given two points is given as follows:

Q: Find parametric equations for the line segment joining the points (9, 8) and (16, 11). O x=9+7t, y…

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Q: Find parametric equations of the normal line to * + y? at the point (2, 2, 5) the surface z= O r =…

A: In this question we have to find parametric equation of the normal line.

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 1 + 6t, z = 2t,…

A: Explanation: Given that,  Line 1: x=1+ty=1+6tz=2t Vector 1: 1,6,2 Line 2: x=1+2sy=5+15sz=-2+6s…

Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

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Q: 3. Find the distance from P(1, 1, 1) to the plane II with equation r – 3y + 4z = 10.

A: Distance between point and plane is (4√26)/13.

Q: Which of the following is the equation of the plane that is tangent to the surface 2 x2 + y? x z –…

A: Given: 2x2+y2-xz-3z=1

Q: b) If we are at the point (1, 2, 4) on the surface z = xy², and we move a short distance in the…

A: Please check step 2 for solution.!

Q: 5. Which of the following is a parametrization of the line through P(-3,2, –3) and Q(1, –1,4) ? |…

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Q: (b) Find the equation of the tangent plane to the hyperboloid r2 + 3y? – 322 = 1 at the point (1,…

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Q: . Find a parametrization for the circle (x – 2)² + y² = 1 starting at (1, 0) and moving clockwise…

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Q: Find a parametric representation of the line through the point P(3,1,-4) and perpendicular to the…

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Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (4, 2, -44).

A: Given: Equation of surface is z=5y2-4x2 and a point -4, 2, -44. To find: Equation of tangent plane…

Q: Find the distance between the skew lines with parametric equations  x = 1 + t, y = 3 + 6t, z = 2t,…

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Q: Find the coordinates of the point(s) on the curve 2y = 10 – a² that are closest to the origin. а) О…

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Q: Which of these describes a parametrized line perpendicular to the plane 3x + 2y + z = 15? A) (2 +…

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Q: Calculate y°dz – yz²dy – sen(2)dz, where C'is the path connecting the point A(-2, 2, 4) to the point…

A: We will calculate the integral ∫Cy2dx-yz2dy-sinzdzwhere path starts from point A-2,2,4 to the point…

Q: Find parametric equations for the line segment joining the points (-6, 4) and (2, 3). x=-6 + 8t, y =…

A: Parametric equation of line segment.

Q: (b) Find the points on the line r(t) = (t, 1+2t, 1-2t) whose distance from the plane 2x - 2y+z=1 is…

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Q: Find a parametrization r(t,s) for the plane which contains the point P(-9, 7, 1) and the line…

A: Use plane concept

Q: Find the equation of the plane that passes through the point (2, 1, 1) and is tangent to the surface…

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Q: parametrization for the line segment beginning at P1 and ending at P2. P 1(-4, 0, 3) and P 2(0, 5,…

A:

Q: Which of these describes a parametrized line perpendicular to the plane 3x + 2y + z = 15? a)…

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Q: Find the points on the hyperboloid 9x^2  - 45y^2 + 5z^2 = 45 where the tangent plane is parallel to…

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Q: Verify that the line r(t) = [1 + t, 1 - t, t] is part of the one sheeted hyperboloid x^2 + y^2 -…

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Q: Which of the following is a parametrization of the line through P(-3, 2, –3) and Q(1, –1, 4) ? (a) x…

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Q: Find a parametrization for the line segment beginning at P1 and ending at P2. P 1(7, 2, 4) and P…

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Q: Find the value of d in the equation of the plane ax+by+cz+d=0 passing through the point P(3, 1, -2)…

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Q: Q2) Find the distance from the point P (1, 2, 3) to the plane x-3y + 2z= 4.

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Q: Find parametrizations for the lines in which the planes x - 2y + 4z = 2, x + y - 2z = 5

A: Given the planes :- x - 2y + 4z = 2,  x + y - 2z = 5   The Arbitrarily set z =1 and solve the…

Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2, - 5) and…

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