Let L be the line in R joining the points (-1, 5, 1) and (1,6, -3)....

 

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Let L be the line in R joining the points (-1, 5, 1) and (1,6, -3). Let P be the plane in R3 with general equation 2x - y + 3z = 5. Let Q be the plane that intersects L at the point (1, 6, -3), and Q intersects L at a right angle. (a) (2 marks) Find the point of intersection of L and P. (b) (2 marks) Find the general equation of the plane Q. (c) (2 marks) Find the angle of intersection of P and Q. (d) (2 marks) Determine whether LPnQ is a line, a point, or the empty set. Let L be the line in R joining the points (-1, 5, 1) and (1,6, -3). Let P be the plane in R3 with general equation 2x - y + 3z = 5. Let Q be the plane that intersects L at the point (1, 6, -3), and Q intersects L at a right angle. (a) (2 marks) Find the point of intersection of L and P. (b) (2 marks) Find the general equation of the plane Q. (c) (2 marks) Find the angle of intersection of P and Q. (d) (2 marks) Determine whether LPnQ is a line, a point, or the empty set.