(a) For which values k are u = (2, 1, 3) and v = (1, 7, k) orthogonal?
(b) Find u dot v given that llu + vll = 1 and llu-vll = 5.
Matrix
2013-12-10 7:12 am
回答 (1)
2013-12-10 11:53 pm
✔ 最佳答案
(a)u = (2, 1, 3) and v = (1, 7, k) are orthogonal if and only if
u ● v = 0
2*1 + 1*7 + 3*k = 0
9 + 3k = 0
k = -3
(b)
|| u + v ||² = (u + v)●(u + v) = u●u + 2u●v + v●v = 1 ...[1]
|| u - v ||² = (u - v)●(u - v) = u●u - 2u●v + v●v = 25 ...[2]
[1] - [2] gives
4 u●v = -24
u●v = -6
收錄日期: 2021-04-13 19:50:54
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20131209000051KK00221