1. Consider the lines l1: x=1+2t, y=1-t, z=3t, t R, x-1 y+2 l2: =1 = 2-5,...

   

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1. Consider the lines l1: x=1+2t, y=1-t, z=3t, t R, x-1 y+2 l2: =1 = 2-5, 2 -1 the plane and the point P(1,0,2). II: x+2y+3x+3=0, (a) Find the point Q of intersection of line 2 and the plane II. (b) Either find an equation of the plane which is perpendicular to the plane II and passes through the points P and Q, or explain why such a plane does not exist. (c) Do the lines and l2 intersect each other? If so, find the point of their intersection. (d) Are the lines 1 and 2 parallel to each other? Explain. (e) Either find an equation of the plane containing the line that is also parallel to the line (2, or explain why such a plane does not exist. (f) Either find an equation of the plane containing the line that is also perpendicular to the line (2, or explain why such a plane does not exist. (g) Find both parametric and symmetric equations (if possible) for all lines which are parallel to the plane II and pass through the point P. 1. Consider the lines l1: x=1+2t, y=1-t, z=3t, t R, x-1 y+2 l2: =1 = 2-5, 2 -1 the plane and the point P(1,0,2). II: x+2y+3x+3=0, (a) Find the point Q of intersection of line 2 and the plane II. (b) Either find an equation of the plane which is perpendicular to the plane II and passes through the points P and Q, or explain why such a plane does not exist. (c) Do the lines and l2 intersect each other? If so, find the point of their intersection. (d) Are the lines 1 and 2 parallel to each other? Explain. (e) Either find an equation of the plane containing the line that is also parallel to the line (2, or explain why such a plane does not exist. (f) Either find an equation of the plane containing the line that is also perpendicular to the line (2, or explain why such a plane does not exist. (g) Find both parametric and symmetric equations (if possible) for all lines which are parallel to the plane II and pass through the point P.