A plane in R³ contains the point (-r, 0, 1) and has the vector (1,4,3r) as a normal, where r is a real number. (a) Determine the equation of the plane in terms of r. (b) Given that the point (0, -2, 2) also lies in the plane, determine the equation of the plane. (c) Find the point of intersection of the plane with the y-axis.

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Q: b) Find parametric and vector equations for the line through (2,3,0) perpendicular to the vectors u…

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Q: - 3)² = 81 then, find its ce or a=<3, -1

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Q: Given the points A(3,-1,1), B(2,3,4) and C(4,1,1). (a) Find a unit vector that is simultanously…

A: Concept: A plane going through three non-collinear points has the following equation: Vectors and…