math?

In1-4 computeV+Wand2V-3WandIVI2andV Wand cos 8.

1v=(1,1,1)'w=(-1, -1, -1)

2 V=i+j, W=j-k

3 V=i-2j+k, W=i+j-2k

4 V=(l, 1, 1, l), W=(l, 2, 3,4)

17-20

17 Describe all points (x, y) such that v = xi +yj satisfies

(a)Ivl=2

(b)Iv-il=2

(c)v0i=2

(d)vWi=lvl

20 IfP=(0,O)andR=(0,1)chooseQsotheanglePQRis 90". All possible Q's lie in a _____________ .

25+26

25. (a) If A and B are unit vectors, show that they make equal angles with A +B.

(b)If A, B, C are unit vectors with A+B+C=0, they form a triangle and the angle between any two is

26. (a) Find perpendicular unit vectors I and J in the plane that are different from i and j.

(b)Find perpendicular unit vectors I, J, K different from i, j, k.

29+38

29 (a)Find the position vector OP and the velocity vector PQ when the point P moves around the unit circle (see figure) with speed 1. (b) Change to speed 2.

38 The point 3 of the way along is the same for all three medians. This means that A +$M3= 3M, = .Prove that those three vectors are equal.

Chapter 12

1-4

1 Sketch the curve with parametric equations x = t, y = t3. Find the velocity vector and the speed at t = 1.

2 Sketch the path with parametric equations x = 1+t, y = 1 - t. Find the xy equation of the path and the speed along it.

3 Onthecirclex = cost,y = sintexplainbythechainrule and then by geometry why dyldx = -cot t.

4 Locatethehighestpointonthecurvex=6t,y=6t-t2. This curve is a , What is the acceleration a?

15-23

15 (a) How far apart are the two parallel lines x = y and x = y + l?

(b) How far is the point x = t, y = t from the point x = t, y = t + I?

(c) What is the closest distance if their speeds are different:x = t, y = t and x ='2t, y = 2t +l?

23 Find the minimum and maximum speed if x = t +cos t, y = t -sin t. Show that la1 is constant but not a. The point is going around a circle while the center is moving on what line?