Which sets of vectors are orthogonal? Check all that apply.a = 〈–1, 0〉 and b = 〈1, 0〉c = 〈1, 0〉 and d = 〈0, –1〉e = 〈–4, –6〉 and f = 〈12, 8〉g = 〈4, –6〉 and h = 〈12, 8〉 v = 〈10, –5〉 and w = 〈–10, –20〉x = 〈10, –5〉 and y = 〈–10, –2〉
Answer
A
a = 〈–1, 0〉 and b = 〈1, 0〉
B
c = 〈1, 0〉 and d = 〈0, –1〉
C
e = 〈–4, –6〉 and f = 〈12, 8〉
D
g = 〈4, –6〉 and h = 〈12, 8〉
E
v = 〈10, –5〉 and w = 〈–10, –20〉
F
x = 〈10, –5〉 and y = 〈–10, –2〉
Explanation
Two vectors are orthogonal when their dot product is 0. For choice B, (1)(0) + (0)(−1) = 0; for choice D, (4)(12) + (−6)(8) = 48 − 48 = 0; and for choice E, (10)(−10) + (−5)(−20) = −100 + 100 = 0. The other choices have nonzero dot products, so they are not orthogonal.
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