Find the symmetric equation the line through the two points

NAME (Neatly):

UID (Neatly):

1. Given the vectors:

¯a = 2ˆı + 6ˆ − 4ˆk
¯b = 0ˆı − 3ˆ + 6ˆk
¯c = 3ˆı + αˆ + αˆk

2. Find the distance between the point (1, 2, 3) and the plane 2x + 3y − 2z = 10. Simplify. Solution: 3. Find aT (1) for the curve with parameterization:

4. Suppose an object follows the path given by the parameterization:

¯r(t) = (3t − 1)ˆı + 2tˆ + tˆk And given the plane with equation:

¯r(t) = sin(πt)ˆı + t2ˆ + 5ˆk	with		[5 pts]
(a) Is the parameterization closed? Justify.	with		[5 pts]

Solution:

	[15 pts]

x − 1 2

(a) x2+ y2+ (z − 2)2= 4 Solution: (b) y = 3

	for	0 ≤ t ≤ π	[5 pts]
Solution:	for	0 ≤ t ≤ π	[5 pts]