a) Find the equation of the plane containing the points P(3, 1, 5), Q(- 1,– 1,– 1), and R(– 2,2, 4).

Q: .Find the equation and sketch the plane that contains the points (2, 6, 1), (-4, 9, -1) and (4, 3,…

A: Equation of plane is 3x+2y+6z = 12

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 an equation of the plane passing through the three points given.P = (5, 1, 1), Q = (1, 1, 2), R…

A: GivenP=(5,1,1) , Q=(1,1,2) and R=(2,1,1)To find equation of plane passing through the three points.

Q: Find an equation for the line that is orthogonal to the plane 3x- y+ 2z =10 and goec through the…

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Q: 1. Find the equation of the plane that contains the following points. (2, –1, 4), (3, 2,0), and…

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Q: Find an equation of the plane through the points P(0, 1, 1), Q(1, 1,1), and R(1,1,0). Write the…

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Q: 3. Find an equation for the plane in R³ containing the points P = (4, 1, 0) Q=(3, 2, 1) R = (5, 1,…

A: The given points are, P=(4,1,0)Q=(3,2,1)R=(5,1,1). Let an equation containing three points…

Q: (11) Find the equation of the plane through points P(5, –2, – 14), Q(-3, –4, 20), R(-1, –2,4).

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Q: Find an equation for the plane through P(1,4,4) that contains the line of intersection of the planes…

A: Let the equation of the plane that contains the line of intersection of the planes 3x-y+3z=-1 and…

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: Please answer asap thank you

A: SO=4x+8, OF=x+14, FT=2x+14, and TS=3x+4 As the definition of parallelogram, the opposite side of…

Q: Find the equation of the plane that contains the line r¡(t) = (1 + lt, –1+t, 2+ 8t) and the point…

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Q: (1) Find an equation of a plane that goes through (-1,2,6) and is perpendicular to (2, 1, –3).

A: It is given that the perpendicular vector to the plane is given as,  and plane passing through,…