Fall 2022 32A-4 Second Midterm
Full Nam e:
UIN:
Circle the nam e of your TA and the day of your discussion:
Gurkiran Dhaliwal Benjamin Major Advika Rajapakse
Tuesday Thursday
INSTRUCITONS
• Read each Problem carefully.
• To get credit for a Problem, you must show all of your reasoning and calculations.
• Box your final answer.
• No calculators are allowed.
• You are allowed to use your formula sheet. The sheet should be hand-written, one-
sided, and of letter size.
• You may use the pages 3, 5, 7, 9, 11 for scratch work. Work found on those pages will
not be graded unless clearly indicated in the exam.
• Th er e w ill be 6 Pr oblem s in the exam . Problem 6 is True or False.
Problem Points Scores
1 10
2 15
3 15
4 15
5 10
6 10
Total 75
1
, Pr oblem 1 (10 points). Consider the paths
→r 1 (t) = ⟨t, t2, t3⟩, →r 2 (t) = ⟨4t2, −8t3, −2t⟩.
1. (5 points) Determine whether they collide, and if they do, determine all the collision
point(s).
2. (5 points) Determine whether they intersect, and if they do, determine all the inter-
section point(s).
2
Full Nam e:
UIN:
Circle the nam e of your TA and the day of your discussion:
Gurkiran Dhaliwal Benjamin Major Advika Rajapakse
Tuesday Thursday
INSTRUCITONS
• Read each Problem carefully.
• To get credit for a Problem, you must show all of your reasoning and calculations.
• Box your final answer.
• No calculators are allowed.
• You are allowed to use your formula sheet. The sheet should be hand-written, one-
sided, and of letter size.
• You may use the pages 3, 5, 7, 9, 11 for scratch work. Work found on those pages will
not be graded unless clearly indicated in the exam.
• Th er e w ill be 6 Pr oblem s in the exam . Problem 6 is True or False.
Problem Points Scores
1 10
2 15
3 15
4 15
5 10
6 10
Total 75
1
, Pr oblem 1 (10 points). Consider the paths
→r 1 (t) = ⟨t, t2, t3⟩, →r 2 (t) = ⟨4t2, −8t3, −2t⟩.
1. (5 points) Determine whether they collide, and if they do, determine all the collision
point(s).
2. (5 points) Determine whether they intersect, and if they do, determine all the inter-
section point(s).
2
