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Numerade Educator

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Problem 23 Easy Difficulty

Determine whether the given vectors are orthogonal, parallel, or neither.

(a) $ a = \langle 9, 3 \rangle $ , $ b = \langle -2, 6 \rangle $
(b) $ a = \langle 4, 5, -2 \rangle $ , $ b = \langle 3, -1, 5 \rangle $
(c) $ a = -8i + 12j + 4k $ , $ b = 6i - 9j - 3k $
(d) $ a = 3i - j + 3k $ , $ b = 5i + 9j - 2k $

Answer

a) The two vectors are orthogonal
b) neither
c) parallel
d) The two vectors are orthogonal

Discussion

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Video Transcript

one of these air thought General parallel or neither. We need to take the dot product. So for a a dot be, it's going to be nine times negative, too. Plus three times six get negative eighteen plus eighteen and that zero. So these air orthogonal hey dot b For the second one, we've got four times three plus five times negative one plus native two times five is is twelve minus five minus ten negative three. Neither a Times B or ADA P Negative. Eight times six plus twelve times negative. Nine plus four times negative. Three. We've got negative forty eight minus twelve minus one. Oh eight minus twelve and I don't know what this is. It's not going to matter, really, because it's neither. It's not zero, and it's not blood. Last one here got three times five less negative one times nine plus three times negative too. Fifteen minus nine minus five That zero. So we are exactly are talking