Question

Find an equation of a plane containing the line r = ⟨−5, 1, 0⟩ + t ⟨7, −8, 4⟩ which is parallel to the plane 4x + 1y −5z = −24.

Answer 1

1-Find an equation of the plane.

The plane that passes through (8,0,-1)

and contains the line x=4-4t , y=1+5t , z=4+2t

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2-Find an equation of the plane.

The plane that passes through the point (-2,2,2)

and contains the line of intersection of the planes

x+y-z=3 and 3x-y+5z=5

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3-Find an equation of the plane.

The plane that passes through the line of intersection of the planes x-z=1 and y+2z=2

and is perpendicular to the plane x+y-4z=3

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4-Where does the line through

(1, 0, 1) and (4,-2,3)intersect the planex + y + z = 8 ?