Answers

Exercise A:

end = start + v

end = (3, 6, 7) + (1, 5, 10)

end = (4, 11, 17)

Exercise B:

v = (10, 18, 3) – (1, 9, 5)

v = (9, 9, -2)

t = 0.5

point = (1, 9, 5) + 0.5 * (9, 9, -2)

point = (1, 9, 5) + (4.5, 4.5, -1)

point = (5.5, 13.5, 4)

Exercise C:

start position = (2, 3, 4) – (5, 5, 3) = (-3, -2, 1)

t = 0.75

point = (-3, -2, 1) + 0.75 * (5, 5, 3)

point = (-3, -2, 1) + (3.75, 3.75, 2.25)

point = (0.75, 1.75, 3.25)

Exercise D:

(8, 2, 3) x (1, 2, 3) = (2*3 – 3*2, 3*1 – 8*3, 8*2-2*1)

= (0, -21, 14)

(1, 2, 3) x (8, 2, 3) = (2*3 – 3*2, 3*8 – 1*3, 1*2- 2*8)

= (0, 21, -14)

These two vectors are direct opposites. They are parallel but pointing in opposite directions, which is what you expect from the two normals. You can tell this by looking at the x, y, and z values, each of which has the same values but is signed differently.

Exercise E:

To begin solving this, you need two...