Question

3. Consider the following two lines:

x = c + t, y = 1 + t, z = 5 + t and x = t, y = 1 - t, z = 3 + t.

Is there a value c that makes the two lines intersect? If so, find it. Otherwise, give a reason.

4. A particle starts at the origin and moves along the shortest path to the line determined by the two points P =(1,2,3) and Q =(3,-2,-1).

(a) Find the location where the particle hits the line.

(b) If the particle moves with constant speed and reaches the line in 2 seconds. Parameterize its motion of the first 2 seconds.

5. With each stated property, give an example of the 2-space vector field F(x,y).

(a) F has a constant direction, but ||F|| increases when moving away from the origin.

(b) F is perpendicular to the vector field <x,2> and ||F||=5 everywhere.

Answer 1