Find An Equation Of The Plane Thatcontains The...

EliteMath1

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Find an equation of the plane thatcontains the line x = 5-3 t, y = -3+t, z = 4 t and is parallel to the plane -4 x-32 y+5 z = 8. Leave your answer in the form A x + B y + C z = D, where A, B, Care integers. Answer:

 

Answer No.1

Anonymous

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Answer No.2

Anonymous

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Since the dot product of the line direction and the normaldirection of the plane is zero then they are orthogonal and thereis a plane containing the line parallel to the given plane. <-3, 1, 4> dot <-4, -32, 5> = 12 - 32 + 20 = 0 the direction of the plane must be <-4, -32, 5>, if wechoose the point with t = 1 from the line we have (2, -2, 4) plugging this into the formula for a plane we have... -4(x - 2) -32(y + 2) + 5(z - 4) = 0 -4x - 32y + 5z = -8 + 64 + 20 -4x - 32y + 5z = 76 check by testing another point from the line (t =2): (-1, -1, 8) -4(-1) - 32(-1) + 5(8) = 4 + 32 + 40 = 76

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