Packet 11: Bonus 14
Four Supreme Court justices expressed fascination with the word “orthogonal” during a 2010 oral argument. For 10 points each:
[10e] Name this mathematical operation that outputs zero when two vectors are orthogonal. This operation sums the product of corresponding terms in two vectors to produce a scalar.
ANSWER: dot product
[10h] The Gram-Schmidt process to find orthogonal basis vectors repeatedly subtracts the results of this operation from a vector.
ANSWER: projection [accept vector projection or proj]
[10m] For an orthogonal basis, this mathematician’s formula rewrites any vector as a linear combination of the basis. A series named for this man transforms periodic functions into sums of sines and cosines.
ANSWER: Joseph Fourier [Jean-Baptiste Joseph Fourier; accept Fourier formula or Fourier series]
<Science - Math, Vikram Narasimhan> | VAULT II Packet 11
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 6 | 18.33 | 67% | 67% | 50% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Exhibition | Chattahoochee B | 0 | 0 | 10 | 10 | M |
| Innovation B | Innovation A | 10 | 10 | 10 | 30 | EHM |
| Johns Creek | Lambert B | 10 | 10 | 10 | 30 | EHM |
| Lambert A | Hoover | 0 | 0 | 0 | 0 | |
| Northview A | Chattahoochee A | 10 | 10 | 10 | 30 | EHM |
| Northview B | Midtown | 10 | 0 | 0 | 10 | E |
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| VAULT II at Georgia Tech | 2026-01-24 | ✓ | 6 | 18.33 | 67% | 67% | 50% |
| VAULT II at UCSB | 2026-03-13 | ✕ | 4 | 25.00 | 75% | 100% | 75% |
| VAULT II at Harvard | 2026-04-30 | ✕ | 4 | 10.00 | 75% | 25% | 0% |
| VAULT II Stanford Online | 2026-07-17 | ✕ | 8 | 15.00 | 75% | 63% | 13% |