CSE 681
Autumn 2009

Homework #1

• Hand in hardcopy at the beginning of class, Wednesday, September 30.

• You can use a calculator to do the actual computations but you must show how you set up the computations in order to receive credit.

PROBLEMS:

1. (2 pts) Compute the cosine of the angle between the 2 vectors.

   V1 = (5, 10)
   V2 = (-2, 20)
   

2. (2 pts) Compute the distance from the point and line.

   P = (5, 10)
   L = ( (2,10), (3, 7) )
   

3. (3 pts) Compute the reflectance vector given:

   incoming ray = (2,3,4)
   normal vector = (1,-3, 4)
   

4. (4 pts) Write down the 4x4 matrix for a y-axis rotation of 30 degrees; sin(30) = .5; cos(30) = .87 and write down the inverse matrix.

5. (2 pts) Write down the 4x4 matrix for a translation of (1,5,-2) and write down the inverse matrix.

6. (2 pts) write down the 4x4 matrix for a uniform scale of 2.5 and write down the inverse matrix.

7. (2 pts) write down the 4x4 matrix for a non-uniform scale of (1,4,2) and write down the inverse matrix.

8. (3 pts) Write down the 4x4 matrix that results when the matrix of #4 is multiplied on its right by matrix of #5 (rotation matrix x translation matrix)