Find an equation of the plane with the given characteristics. The plane passes through the point (10, -8, 5) and contains the line given by y – 4 2 = z.

Q: Find the equation of the plane with the given description. Passes through (6, 1, 5) and is parallel…

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Q: Find an equation of the plane that passes through the points A(2, 1, 1), B(-1, -1, 10), and C(1, 3,…

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

Q: Find an equation for the plane that contains the line v = (-1, 1, 2) + t(9, 5, 4) and is…

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Q: Find the equation of the plane that passes through the point (6, 0, −2) and contains a straight r:…

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Q: Find the equation of the plane through the point P= (3,3,5) and parallel to the plane y – 5x + 5z =…

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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: Find an equation of the plane that contains the point P(5,0,2) and the line x = 3t +1, y=-2t + 4, z…

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Q: Find the equation of the plane through the point P= (2,4, 5) and parallel to the plane - (5x + 3y +…

A: Parallel plane problem....

Q: Find the equation of the plane parallel to the intersecting lines (1,2 +t, -3 – 3t) and (1 – t, 2 –…

A: Let, the direction vector of 1,2+t,-3-3t is v1=0,1,-3 and the direction vector of 1-t,2-3t,-3-2t is…

Q: find an equation for the plane through pointsP, Q, and R. P(1, 0, 0), Q(0, 1, 0), R(0, 0, 1)

A: Given points are Here the objective is to find the equation of the plane passing through points P,…

Q: Find the equation of the plane that contains the point P(3,5,-1) and the linex = 4 - ty = -1 + 2t,z…

A: The plane contains the point P(3,5,-1) and the line x=4-t, y=-1+2t, z=-3t

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

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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 form ar+by+cz = d for the plane that passes through the points A(3,2,0),…

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Q: Find an equation of the plane. The plane that passes through  (6, 0, −3)  and contains the line  x =…

A: The plane passes through a point P=(6,0,-3) and contains the line x=2-4t, y=1+5t, z=6+4t. Hence, we…

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: Find an equation of the plane that is parallel to the plane x + 7y – 2z + 20 = 0 and contains the…

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

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Q: GIVE AN EQUATION OF THE PLANE DESCRIBED BELOW (A. ) containing (-5, 2, 4) and perpendicular to the…

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Q: Find an equation for the plane that contains the line x = − 1 + 3t, y = 5 + 3t, z = 2 + t and is…

A: We need to determine the equation of the plane that contains the line: x=-1+3t, y=5+3t, z=2+t and is…

Q: Find the equation of the plane with the given description. Passes through P = (3, 5, −9) and is…

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Q: Find an equation of the plane that contains the point (2, 0, 3) and the line x =-1+t, y =t, z=-4+21…

A: It is given that the required plane contains the point 2,0,3 and the line x=-1+t,y=t,z=-4+2t. The…

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

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Q: Give the general equation of the plane containing the point (3,-1,4) and 2-2 -3 4. | perpendicular…

A: given plane pass through the point(3,-1,4)

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. The plane through the point (-3, 9, 10) and perpendicular to the line…

A: Find the equation of the plane

Q: Find an equation of the plane containing the point P(1, -2, -2) perpendicular to the line through…

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Q: Find the equation of the plane with the given description. Contains the lines r1(t) =〈2, 1, 0〉+〈t,…

A: Find the equation of plane containing two lines: r1t=2,1,0+t1, 2, 3 and r2t=2,1,0+t3, 1, 8.…

Q: Find an equation for the plane that passes through the point (1, 3, -5) and is perpendicular to the…

A: Given point is (1,3,-5). The scalar equation of a plane that passes through point (a, b, c) and has…

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 an equation of a plane passing through the points (1, –1, 7), (3, 2, –20) and perpendicular to…

A: Here we use elimination process.

Q: Find an equation for the plane that passes through the following points. (2, –1, 4), (0, 0, 6), and…

A: Explanation of the solution is given below...

Q: Find the equation of the plane which contains the line ( 2 + t , 3 − t , 4 + 2 t )and the point ( 0…

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Q: Find the equation of a plane through the point (3, -2, 8) and parallel to the plane z=x+ y.

A: Given, Plane is passing through the point (3, -2, 8) and Parallel to the plane z=x+y    Equation of…

Q: a) Find an equation of the plane passing through the points P=(1,–2,0),Q=(3,1,4) and R = (0, –1,2).

A: Given points are P1,−2,0, Q3,1,4, R0,−1,2. We have to find the equation of the plane passing through…

Q: Find the equation of the plane contains the line x=3t,y=1+t, z=2t, and parallel to the line of…

A: Given, the plane contains the lines x = 3t, y = 1 + t, z = 2t and parallel to the line of…

Q: Find the equation of the plane whose has the line x=2-3t, y=3 + t, z = 5t and passes through the…

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Q: Find an equation for the plane passing thnrough the given points: Р(- 4, — 1, — 1), Q(- 2, 0, 1). R(…

A: Given that: Points P(-4,-1,-1), Q(-2,0,1), R(-1,-2,-3)

Q: Find an equation of the plane that is parallel to the plane x+ 2y – 10z + 12 = 0 and contains the…

A: The equation of the given plane is  x+2y-10z+12=0 We need to find the equation of plane that is…

Q: Determine an equation for the plane that passes through the point (1, 2, –3) and is parallel to the…

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Q: Find the Cartesian equation of the plane containing the points A(1,0,3), B(1,1,-2) and C(-1,2,0).

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Q: Find the equation of the plane that contains the points P(-1,2, 1), Q(0, -3, 2), and R(0, 1,-4)

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Q: Find an equation of the plane that contains the point (2,0,-8) and contains the line y- 2 z+1 x +4 =…

A: The plane passes through the point 2, 0, -8. Thus, the equation of the plane can be written as…

Q: Find the equation of the plane through the point P = (5, 3, 3) and parallel to the plane 3y – 5x –…

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Q: Find an equation of the plane. The plane that passes through the point (2, 4, 5) and contains the…

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Q: Find the equation of the plane that contains the point P(3,5, –1) and the line = 4 – t, y = –1+ 2t,…

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Q: The equation of the plane passing through the point A(4, 9, 4) and orthogonal to the line a = 9 +…

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