1) Determine whether the points below lie on a straight line. If they do not lie on a straight line d they determine a right triangle?
(3, -6, 1), (5, 4, -1), (4, -1, 0)
2) Describe in words the region of R3 represented by the equation y2+ z2 = 16.
3) A sled is pulled horizontally over ice by a rope attached to its front. A 20-lb force acting at an angle of 60° with the horizontal moves the sled 100 feet. Find the work done.
4) Find AB' if A = (2,3,5) and B = (-1, 2, 7).
5) Let a=<6,3,-2> and b=.<2,1,2>
a) Find |a|
b) Find a.b
c) Find the angle between a and b
d) Find the direction cosines of a.
e) Find the scalar projection of b onto a.
f) Find the vector projection of b onto a.
g) Find a x b