Kometaki Okaka is a somewhat bizarre student: he sings strange songs, hangs around with the school's resident weirdos, likes to watch ugly girls, and enjoys puzzles.
His school is undergoing a somewhat bizarre series of events: classrooms keep moving, students and teachers are losing hours of memory, and one student is even attacked.
Okaka and the school's weirdness meet each other head on when he sees a late student, Takano, being chased by a giant lizard monster. A fellow student, Nitta, attempts to take down the monster, but is ultimately beaten down. Okaka manages to save both of them though, using his prowess with puzzles to trap the monster in a cage of desks, which pins it down long enough for Nitta to destroy it.
It turns out the school's students are being targetted by creatures from another world, who are trying to possess steal the student's bodies in order to take over the world. Nitta was formerly one of them, but has switched sides in order to help his little sister, who is gravely ill.
It is a lot less serious than it sounds.
This Anime/Manga provides examples of:
- The Ace: Okaka is physically fit, able to pull of amazing feats of athleticism, naturally smart without having to study and is able to solve the titular Vector Ball, the hardest of the Spirit Beings puzzles, that tests people's capabilities. Yet, he's still unhappy since his personality makes it impossible for him to make friends until he meets Nita.
- Awesomeness by Analysis: Okaka can tell the measurements of anything he looks at. This is complemented by the titular Vector spirit body, which allows Okaka to convert objects into the exact form he's thinking of.
- Big Guy, Little Guy: Okaka and Nita fits this as the main duo.
- Brains and Brawn: Subverted with Okaka and Nita. Initially Okaka seems like the Big Guy, who fights against the spirit beings with desk and chairs through his sheer physical prowess, while Nita fights by shooting magical lances that he creates out of thin air. It's quickly revealed that Okaka's fighting style is actually based on his aptitude with puzzles and he is quite smart, if eccentric. Nita's battle strategy on the other hand, basically boils down to keep on throwing lances at his opponent until he's able to hit them.
- Childhood Friend: Okaka and his neighbor Matsubara has known each other since childhood and while they don't actually consider each other friends, they both secretly respect or admire the other.
- Gratuitous English: Amerika-sensei's English Conversation Club, a place where japanese students can learn how to... make weird noises."Kakyoin! Iggy! Avdol! It's over!"
- Healing Factor: Okaka is informed that spirit bodies are able to heal themselves and others by spending their power. He then stares off into the distance, wondering why Nita never bothered to heal him...
- Hollywood Homely: In-universe, Okaka likes to laugh at "ugly" girls, and his childhood friend Matsubara apparently falls under that category. Except, she's not so much "ugly" as "plain". Though she used to be Ugly Cute when she was a kid.
- I Just Want to Have Friends: Both Nita and Okaka starts off the serie being completely alone and without friends, but for different reasons. Nita needs to uphold The Masquerade and keeps to himself, so as to not endanger the people around him. Okaka on the other hand, while being naturally talented and coming from a rich family,has trouble making friends because his eccentric behavior makes him come off as a horrible guy.
- Improbable Aiming Skills: Okaka is able to create a "Construction Hell" by making a bunch of objects interlock in a fashion that makes them impossible to pull free from each other. Just making such a construct would be hard enough in and of itself, but Okaka is able to pull it off in the middle of combat, around giant monsters, by throwing objects such as table and chairs at them.
- No Social Skills: Throughout the school Okaka is known as a guy that laughs at ugly girls.