**Chapter 6.1 - An Introduction to Vectors**

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**Chapter 6.2 - Vector Addition**

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**Chapter 6.3 - Multiplication of a Vector by a Scalar**

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**Chapter 6.4 - Properties of Vectors**

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**Mid Chapter 6 Review**

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**Chapter 6.5 - Vectors in R2 and R3**

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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

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**Chapter 6.6 - Operations with Algebraic Vectors in R2**

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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

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**Chapter 6.7 - Operations with Vectors in R3**

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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

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**Chapter 6.8 - Linear Combinations and Spanning Sets**

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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