Exercises 

Define the following vectors: 

a=(2,3), b=(-1,2), c=(4,-3), u=(0,1), v=(2,-4,), w=(,1,-2) 

Using the above vectors, compute the following on a separate worksheet by loading the appropriate package and using the appropriate Maple command. 

1. The magnitude of the following vectors: i) c ii) u iii) v 

2. i) 2a - 3b   ii) u + 2v  

3. i) a ·b  ii) a·c  iii) u·w 

4. i) u×w  ii)w×u  iii)v×w 

5. What happens if you try to compute a·u? What happens if you try to compute a×b? 

6. Suppose you embed a and b in a 3-D space. Define two new vectors that are a and b embedded and compute their cross product. What direction does it go?