HW#8 Ch 3: Vectors
Instructions: Show work for each problem to earn full credit.
1. Three vectors are given by \(\vec a = 2.0\hat i - 3.0\hat j - 1.0\hat k\), \(\vec b = 3.0\hat i - 1.0\hat j - 2.0\hat k\), and \(\vec c = - 1.0\hat i - 2.0\hat j + 2.0\hat k\). Find a) \(\vec a \cdot \left( {\vec b + \vec c} \right)\) and b) \(\vec a \cdot \vec b + \vec b \cdot \vec c\).
2. Find the angle between vectors \(\vec a\) and \(\vec b\) if \(\vec a = 1.0\hat i + 2.0\hat j + 3.0\hat k\) and \(\vec b = 3.0\hat i + 2.0\hat j + 1.0\hat k\).
3. Two ants run across a flat table, starting at the same point. Ant 1 runs 0.30 m due east, then 0.20 m at 30° north of due east. Ant 2 also makes two runs; the first is 0.1 m at 50° east of due north. What must be a) the magnitude and b) the direction of its second run if it is to end up at the new location of ant 1?
4. In 2004, the Spirit of Ontario set out from a southern point on Lake Ontario for a point on the Canadian side near Toronto, 152 km due north. If there was a 20 km/h wind heading 20° south of east, a) in what direction must the ferry have headed to reach its destination if its average speed was 70.0 km/h? b) How long did it take to get there?