Group 2 – Test #2 Solutions

4 Comments

1. 

   Simon Lin

   April 27, 2026 at 11:07 pm

   Problem 1

   Score:  

   Notes: The group correctly identified that a non-zero determinant for the coefficient matrix implies a unique solution. And finding the value x = -5 using Cramer’s rule

   Problem 2

   Score:  

   Notes: The components of the vector PQ were correctly calculated by subtracting P from Q to get <-4, -2, 1>. The norm ||PQ|| =√21 and the resulting unit vector u were both derived accurately. 

   Problem 3

   Score:  

   Notes: The group has the right idea regarding vector addition and navigation through the diagram. For example, part (e) correctly demonstrates the tip-to-tail method: AB +BC – OC= AC+ CO = -u – v. 

   Problem 4

   Score:  

   Notes: The solution is perfect and exhaustive. The group correctly calculated:

   • The dot product is 6.
   • The vector projection projv (u) = <18/35, -6/35, 30/35>
   • The cross product u x v = <4,-23,-7>
   • The angle ፀ≈76.17°
   • Verification that the cross product is orthogonal to the original vectors

   Problem 5

   Score:  

   Notes: The work is perfectly executed. The group established the correct parametric equation for the line and then accurately checked if the point (-11, -8, -1) existed on that line by solving for the parameter $t$. They correctly found that t = -2 consistently satisfies all three coordinate equations. 

   Problem 6

   Score:  

   Notes: The group correctly answered the conceptual True/False questions and provided valid examples for (b) and (e), counterexamples for (a), (c), and (d) 

   Problem 7

   Score:  

   Notes: All examples provided are correct and demonstrate a clear understanding of the concepts. The group successfully found a point Q for a given vector, provided two orthogonal vectors with a zero dot product, and correctly constructed a unit vector that was not a standard basis vector.

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2. 

   Simon Lin

   April 27, 2026 at 11:10 pm

   Idk why the stars are so big, but all of them are solutions are correct

   Reply
   • 

     Kate Poirier

     April 28, 2026 at 1:20 pm

     Haha enormous stars are great!

     Reply
3. 

   Simon Lin

   April 27, 2026 at 11:10 pm

   Group Member: AHR, SL, CT, SCC

   Reply