1. Consider the three points P(1,0, 2), Q(-2, 1, 4), and R(2, -2,2). (a) Compute PQ PR. Show your steps for this process. (b) Find the equation of the plane passing through the points P, Q, and R.

Q: Find the equation of the plane parallel to the intersecting lines (1,2 +t, -3 – 3t) and (1 – t, 2 –…

A: Let, the direction vector of 1,2+t,-3-3t is v1=0,1,-3 and the direction vector of 1-t,2-3t,-3-2t is…

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: Find an equation for the plane that contains the line v = (-1,2,7) + t(3,2, 4) and is perpendicular…

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Q: Find the equation of the plane containing the point P = (6,8, -12) that is parallel to the plane 6x…

A: The plane containing the point  that is parallel to the plane .The objective is to find the equation…

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: Which of the following equations define the plane passing through the points (3,0, 0), (0, –7,0),…

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Q: Determine the equation of the plane through the points (1, 0, 3) and the line l : ¯r = (3, 4, 1) +…

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Q: Find the equation of the plane that contains both of the lines given below. Line 1: x = 1+t, y = 2+…

A: Line 1 : x=1+t, y=2+2t, z=3-t        ⇒a⇀=1, 2, 3, l⇀=1, 2, -1 Line 2 : x=1-s, y=2+4s, z=3+2s…

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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