# Chapter 6 - An Introduction to Vectors

Chapter 6.1 - An Introduction to Vectors

1. 2. 3. 4. 5. 6. 7. 8. Chapter 6.3 - Multiplication of a Vector by a Scalar

9. 10. 11. Chapter 6.4 - Properties of Vectors

12. 13. Mid Chapter 6 Review

14. 15. Chapter 6.5 - Vectors in R2 and R3

16. 17.     What is the equation of the plane that contains the points A(1, -3, 7), B(1, 2, -8) and C(1, 0, 5)?

Answer:  x = 1                                   Solution to #17

18. 19. 20. Chapter 6.6 - Operations with Algebraic Vectors in R2

21. 22.    Triangle DEF has vertices D(2, -5), E(-1, 3), F(4, 11).  Using side lengths, determine whether DEF is a right triangle.

Answer: Not a right triangle                                   Solution to #22

23.    A parallelogram has vertices at A (5, -4), B(9, 3) and C(2, 7).  Determine all possible coordinates for the fourth vertex.

Answer:  (-2,0) or (6, 14) or (12, -8)                                   Solution to #23

24. 25. Chapter 6.7 - Operations with Vectors in R3

26. 27.    Determine the point on the y-axis that is equidistant from the points P(2, 3, 9) and Q(-4, 7, 11).

Answer:  (0, 11.5, 0)                                               Solution to #27

28. Chapter 6.8 - Linear Combinations and Spanning Sets

29. 30. 31. 32.   Determine the value for y such that A(-4,6,1), B(6,y,3) and C(2,2,5) are on the same plane as D(1,1,2).

Answer: y = -4                                Solution #32

33.   The vectors (a, b, 5), (6, -1, 2) and (-2,2,1) are coplanar.  State the conditions on a and b for which this is true, and then state three sets of values of a and b for which this is true.

Answer:  b = -0.5a + 5, so perhaps a = -10, b = 10 or a = 0, b = 5 or a = 10, b = 0               Solution to #33