Question

At what point do the curves r1 =〈 t , 1 − t , 3 +...

  1. At what point do the curves r1 =〈 t , 1 − t , 3 + t2 〉 and r2 = 〈 3 − s , s − 2 , s2 〉 intersect? Find the angle of intersection.

  2. Determine whether the lines L1 : r1 = 〈 5 − 12t , 3 + 9t ,1 − 3t 〉 and L2 : r2 = 〈 3 + 8s , −6s , 7 + 2s 〉are parallel, skew, or intersecting. Explain. If they intersect, find the point of intersection. If they are parallel or skew, find the distance between them.

  3. For the two vectors a = 〈 −1 − t , 5 − 2t , 7 − t〉 and b = 〈 −1 , −2 , −1 〉. Calculate a × b and |a × b|. What is the geometrical meaning of this result?

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