In Problems 9–18, (a) find the dot product v · w; (b) find the angle between v and w; (c) state whether the vectors are parallel, orthogonal, or neither. 9. v = i - j, w = i +j 10. v = i +j. w = -i +j 11. v = 2i + j. w = i - 2j 14. v = i+ V3j, w = i - j 12. v = 2i + 2j. w = i + 2j 15. v = 31 + 4j, w = -6i - 8j 17. v = 4i, w = j = i+j 16. v = 3i - 4j, w = 9i – 12j 18. v = i, w = -3j 13. v = V3i – j. w =

Linear Algebra: A Modern Introduction
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Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
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In Problems 9–18, (a) find the dot product v · w; (b) find the angle between v and w; (c) state whether the vectors are parallel, orthogonal,
or neither.
9. v = i - j, w = i +j
10. v = i +j. w = -i +j
11. v = 2i + j. w = i - 2j
14. v = i+ V3j, w = i - j
12. v = 2i + 2j. w = i + 2j
15. v = 31 + 4j, w = -6i - 8j
17. v = 4i, w = j
= i+j
16. v = 3i - 4j, w = 9i – 12j
18. v = i, w = -3j
13. v = V3i – j. w =
Transcribed Image Text:In Problems 9–18, (a) find the dot product v · w; (b) find the angle between v and w; (c) state whether the vectors are parallel, orthogonal, or neither. 9. v = i - j, w = i +j 10. v = i +j. w = -i +j 11. v = 2i + j. w = i - 2j 14. v = i+ V3j, w = i - j 12. v = 2i + 2j. w = i + 2j 15. v = 31 + 4j, w = -6i - 8j 17. v = 4i, w = j = i+j 16. v = 3i - 4j, w = 9i – 12j 18. v = i, w = -3j 13. v = V3i – j. w =
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