Write a parameterization r(u, v) for the given surface. Include reasonable bounds for u and v. 10 The plane 6x+3y+4z = 10. 11 The plane containing the three points (1,4,-2), (-3, 0, 1), and (2,4,-5). 12 The portion of the plane 8x+5y + z = 14 that lies in the first octant.

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: Solve the following

Q: Find an equation of the plane that passes through (2, –1, 5) and is parallel to the plane containing…

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Q: Find the distance between the point (-1, 1,-1) and the plane 3x - 5y + 2z = 12

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Q: Find a parametric representation for the surface. the plane that passes through the point (0, -1, 5)…

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Q: Let P = (-2,0, 5), Q = (3, 1, 1), and R = (0,0, 4) and define a = PÓ and b= PR. Find (d) The…

A: Given three points are: P:-2,0,5, Q:3,1,1, R:0,0,4 The position vectors for the given points are:…

Q: 1. Find the distance from the point S(2,-3,4) to the plane x+ 2y+ 2z = 13 2. Find the distance from…

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Q: Surface Plane Point z = V 98 - x? x = 9 (9, 1, 4) 100 100 50 of -50 -100 50 10 10 -50 -100 -10 -10…

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Q: Find an equation for a plane R at a distance 9 from a plane P with equation 2x + 2y - z = 3 .

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Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane a + 2y +…

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Q: Find the distance the point P(2,0,1) is form the plane 3x – 6y + 2z = 15. -

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Q: 4. Find an equation of the plane that passes through the points P(1,3,2), Q(3,–1,6), and R(5,2,0).…

A: Given points P1,3,2, Q3,-1,6, R5,2,0

Q: Give v that is perpendicular to a plane containing (1,2,3), (3, 4, 1) and (-1, -2, -3). Check if…

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Q: Find the equation of the plane that contains the line 2 5-x 2+y – 5 – z, and the 3 point P( 0,5,2).…

A: We have to find the equation of the plane that contains the line and the point.

Q: Question 3. Do the lines x=t, and x = 2t - 2, y = 2t - 1, 2 = 3t+1 intersect each other at only one…

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Q: Suppose C is the triangle with vertices (3, 0, 0), (0, 4, 0), and (0, 0, 1) oriented…

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Q: Find the distance from Po = (3, 9, 6) to the plane 3x + 4y – 5 = 0.

A: The given equation of plane is 3x+4y-5=0 and the point is P0=3, 9, 6. The distance between a point…

Q: Determine the general equation of the plane 2 passing through the point P(1,-4,-5) and parallel to…

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Q: II. Find an equation of the plane containing the points (0,2,-1) and (1,-1,-1) and perpendicular to…

A: we have to find the equation of plane.  Let, a,b c are the direction ratios of required plane 1.

Q: Find the distance the point P(2,0, 1) is form the plane 3x - 6y + 2z = 15.

A: we have to find the distance , the point p(2, 0, 1)is form the plane 3x-6y+2z = 15 i.e 3x-6y+2z-15 =…