Let L1 and L2 be the lines in R defined by: L1: ri(t) = (2 t,...

      

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Let L1 and L2 be the lines in R defined by: L1: ri(t) = (2 t, 2-4t) L2: r2(t)=(-93t, 8+ 3t) (a) Find all solutions of the equation ri(t) = r2(t) (if any exist). (b) Sketch L1 and L2 in the xy plane. Do the lines intersect? If so, at which point(s)? Does this conform with your expectations from part (a)? (c) Explain clearly why solving the equation r(t) = r2(t) it is not sufficient to determine if the lines L and L2 intersect. (d) Let L3, L4, and L5 be the lines in R defined by: L3: r3(t) = (1 + 2t, 1+ 2t, 2 4t) LA: r(t) = (t, t, 2t) L5: r(t) = (1 3t, 2+t, 2t) For each pair of these three lines (i.e. L3 and L4, L4 and L5, and L3 and L5), determine if they are parallel, skew, intersect in a single point, or are the same line, and find all points of intersection (if any exist). Let L1 and L2 be the lines in R defined by: L1: ri(t) = (2 t, 2-4t) L2: r2(t)=(-93t, 8+ 3t) (a) Find all solutions of the equation ri(t) = r2(t) (if any exist). (b) Sketch L1 and L2 in the xy plane. Do the lines intersect? If so, at which point(s)? Does this conform with your expectations from part (a)? (c) Explain clearly why solving the equation r(t) = r2(t) it is not sufficient to determine if the lines L and L2 intersect. (d) Let L3, L4, and L5 be the lines in R defined by: L3: r3(t) = (1 + 2t, 1+ 2t, 2 4t) LA: r(t) = (t, t, 2t) L5: r(t) = (1 3t, 2+t, 2t) For each pair of these three lines (i.e. L3 and L4, L4 and L5, and L3 and L5), determine if they are parallel, skew, intersect in a single point, or are the same line, and find all points of intersection (if any exist).