Day 21 in Mat221

Today:

• Distribute Section 13.5 (part b) Worksheet

• Return 13.3 problems.

• Quiz Opportunity over Section 13.5a

• Questions on old stuff?
  • Problem #45, section 13.4
    • a) - no - consider, for example, two vectors b and c, both perpendicular to a (but not equal); the dot products are both equal however, as zero;
    • b) - no - consider, for example, two vectors b=a and c=2a, both parallel to a (but not equal to each other); the cross-products are both equal however, as the zero vector;
    • c) - yes!
      • a b = a c implies that a (b-c)=0
      • a x b = a x c implies that a x (b-c)=0
      • (b-c) is simultaneously parallel and perpendicular to a; this means that b-c=0, or that b=c
  • From 13.5: #1, 3, 13, 15

• Collect problems 13.4.

• Section 13.5 (part b - planes):
  • worksheet study questions

  • section summary (part b)

  • Problems:
    • #19, 49, 35, 61

Next time: 14.1 - vector functions and space curves