Reference no: EM13281605

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