Find the equation of the plane that passes through the point P = (1, -5, 2) that has normal n = (-4, 1, 2). Write your answer in the general form. O x-5y+2z=-5 O -4x+y+2Z3D10 O -4x+y+2z=-5 O x-5y+2z3-8

Q: Find the plane z = a + bx + cy that best fits the data points (0, -4, 0), (5, 0, 0), (4, –1, 1), (1,…

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Q: b). Find the equation of the plane that passes by P(1, -2,3), Q(1,0,1), and the Origin O(0, 0, 0)

A: We have to find the equation of plane.

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

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Q: Find an equation of the plane. The plane that passes through (7, 0, −4) and contains the line x = 3…

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Q: Determine the equation of the plane passing through the points P(–2, 1, 5) and Q(4, 9,-3) and…

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Q: Find the equation of the plane passing through the points O = (0,0,0), A = (-2,–2,1) and B= (-1,0,…

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Q: Find an equation of the plane that passes through the points M(1,2,3), N(-3,-2,5), and 0(2,-3,4).

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

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Q: 6. Find the equation of the plane that passes through (3,1,2) and (-1,2,–1) and is parallel to the…

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Q: Find an equation for the plane passing through the point P(-2, 1, 1) and parallel to the plane 3x +…

A: Solve for the equation

Q: Find an equation of the plane. The plane that passes through the point (1, 3, 5) and contains the…

A: Given linex=5t , y=1+t , z=3-tDirection vector of this linev⇀=5,1,-1coefficients of t

Q: Find an equation of the plane passing through the three points give P = (4, –1, 2), Q = (1, 1, 1), R…

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Q: Find the equation of the plane through the point (1,2,-1) and parallel to the plane 2x- 3y+4z+6-D0.…

A: To find: The equation of plane passing through the point 1,2,-1 and parallel to plane 2x-3y+4z+6=0.…

Q: 4) Find the equation of the plane that passes through the point (6,0, 2) and contains the line x = 4…

A: The plane that passes through the point (6, 0, 2) and contains the line x = 4 − 2t, y = 3 + 5t, z =…

Q: Determine the equation of the plane passing through the points P(-2, 1, 5) and Q(4,9, -3) and R(3,…

A: To determine the equation of the plane passing through the points P(-2, 1, 5) and Q(4, 9, -3), and…

Q: Which of the given points are the points on the hyperboloid x2-y?+4z2 = 4 where the normal line is…

A: Solution is in step 2

Q: Find an equation of the plane. the plane that passes through (8, 0, -1) and contains the line x = 5…

A: The equation of plane through a point and contains a line

Q: 6. For a plane with a normal of ñ = [1,2,-9] and containing a point P (3,-4, 0), write the scalar…

A: Given: Normal of the plane π is given by, n→=i→ + 2j→-9k→ Point P on the plane is P3,-4,0 To find…

Q: Find the plane z = a + bx + cy that best fits the data points (0, –4, 0), (5,0, 0), (4, –1, 1), (1,…

A:

Q: Find an equation of the plane. The plane that passes through (6, 0, –1) and contains the line x = 2…

A: Given a point (6, 0, -1) and a line x = 2 - 4t, y = 1 + 5t, z = 8 + 4t

Q: Find a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

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Q: Find an equation of the plane. The plane that passes through  (6, 0, −2)  and contains the line  x…

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Q: snip1

A: we have to find the normal and general forms of the equation of the plane that contains the point…

Q: wnd the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given by…

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Q: The plane that passes through  (9, 0, −3)  and contains the line  x = 6 − 3t, y = 2 + 5t, z = 4 +…

A: Given : A point (9,0,-3) where the plane passes through.             A system of equations for line…

Q: Find the linear equation of the plane through the point (1, 7, 6) and parallel to the plane x + 3y +…

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Q: Find an equation of the line passing through Po and normal to the plane P. Po(2,3,4); P: 3x- 2y +z=…

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Q: O Find equations of the line that passes through the point (2,0,3) and is normal to the plane x – 2y…

A: We will find out the required equation of line.

Q: Find an equation of the plane. The plane that passes through (7, 0, –4) and contains the line x = 4…

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Q: Find an equation of the plane through (-8, 6, - 6) that is perpendicular to the planes 9x - y + z =…

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Q: Determine the equation of the plane passing through the points P(-2, 1,5) and Q(4,9. -3) and R(3,…

A: The given points are: P-2,1,5Q4,9,-3R3,-1,0

Q: I need help with this question

A: Let the equation of plane passing through the point A(-1,2,0) is

Q: Find an equation of the plane that passes through the points M(1,2,3), N(-3,-2,5), and O(2,-3,4).

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Q: 1. Find the equation of the plane that passes through the points P(2,0,1), Q(1,0,-1) and R(3,0,1).

A: We have, Vectors in the plane are, Therefore, equation of plane passes through 3 points will be,…

Q: Find an equation of the plane. The plane that passes through the point (3, 4, 5) and contains the…

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Q: Find the linear equation of the plane through the point (0, 1, 1), (1, 0, 1), and (1, 1, O)

A: Consider the point (0,1,1). Take option (a) x-y-z+2=0-1-1+2=0 Take option (b) -x+y-z+2=-0+1-1+2=2≠0…

Q: A normal vector to the plane passing through the point (2, 1, -4) is (-1, 3, -61 The equation of…

A: The objective is to find the equation of plane.

Q: 2. Find the coordinates of the y-intercept of the plane (x, y, z)=(4,6,5) +s(2,3,1) + t(3,6,12)

A: To find out the coordinate of y-intercept.

Q: Z= (a) What is the equation of the plane passing through the points (2, 0, 0), (0, 2, 0), and (0, 0,…

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Q: Find the equation of the plane through the points (3, 1, 2), (1, 0, 0) and (1,2, 3) in R°. Select…

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Q: A normal equation of the plane that contains the line 1₁: (x, y, z) = (1, -1, 2) + t (9, 1, 3), t E…

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Q: Write the equation for the plane through the points P(-1, 1,-12), Q(2, 8, -49) and R(1, -6, 45). 4x…

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Q: Find an equation of the plane that passes through P(4, 2, – 3) and is perpendicular to the line x+1…

A: Given that the plane is passes through the point (4,2,-3) and perpendicular to line x+1-3=y-12=z2

Q: Find the general equation of the plane passing through P(−1, 3, −2) and having n = (−2, 1, −1) as a…

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Q: 3. Find an equation of the plane passing through the points P = (5,1,1), Q = (1,1,2), R = (2,1,1)

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Q: A normal vector to the plane passing through the point (1, 3, -7) is [-2, 1, -51. The equation of…

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Q: Find the equation of the plane passing through the points O = (0,0,0), A = (2,2, –4) and B = (-4,0,…

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

A: Given, The points are P (1, 2, 3), Q(2, 3, 4), R(3, 6, 9).

Q: Find an equation of the plane through the three points given: P=(0,0,3), Q=(2,−3,2), R=(−1,1,0)

A: find the equation of the plane

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.