1. Suppose you are given the following:
a. ⃗ : The position of a train.
b. ̂ : The direction of the tracks.
c. ⃗ : your position
Symbolically determine ⃗ , the closest position the train will ever come to you.
2. Suppose you are given:
a.
: The position of a playing card
̂
b.
: A direction vector pointing in the direction the playing card is facing.
⃗
c.
: Your position
Write a symbolic algorithm to determine (True / False) if you can see the front of the card.
3. Suppose you are given:
a. ⃗ : The player's position (a VectorN object)
b. ⃗⃗ : the mouse's position (a VectorN object)
Write code to draw a circle at the player's position, but draw that circle in dark-grey (64,64,64) if
the mouse is directly to the right, and white (255,255,255) if the mouse is to the left, and
smoothly interpolated in-between.
4. Suppose you are given:
a.
: The direction you are facing (this vector is defined relative to the world coordinate
system)
b. ⃗ : the direction to your right (similar to F)
c. ⃗ : your up direction.
d. : The velocity vector of a vehicle (expressed in miles / hour).
Determine symbolically how fast the car appears (relative to you) going in miles / hour in these
directions: towards you (positive = away from you, negative towards), side-to-side (positive = to
your right, negative = to your left), and up-and-down (positive = up, negative = down).