If a=i+7j+k and b=i+17j+k, find a unit vector with positive first coordinate orthogonal to both a and b.?
2020-07-23 4:45 pm
If a=i+7j+k and b=i+17j+k, find a unit vector with positive first coordinate orthogonal to both a and b.
回答 (3)
2020-07-23 6:27 pm
Let pi + qj + rk be a vector that orthogonal to both a and b.
The vector is orthogonal to a:
(pi + qj + rk) • (i + 7j + k) = 0
p + 7q + r = 0 …… [1]
The vector is orthogonal to b:
(pi + qj + rk) • (i + 17j + k) = 0
p + 17q + r = 0 …… [2]
[2] - [1]:
(p + 17q + r) - (p + 7q + r) = 0
10q = 0
q = 0
Plug q = 0 into [1]:
p = -r
One of the vector is i + 0j - k
The unit vector
= {1/√[1² + (-1)²]} (i + 0j - k)
= (1/√2)i + 0j - (1/√2)k
The vector is orthogonal to a:
(pi + qj + rk) • (i + 7j + k) = 0
p + 7q + r = 0 …… [1]
The vector is orthogonal to b:
(pi + qj + rk) • (i + 17j + k) = 0
p + 17q + r = 0 …… [2]
[2] - [1]:
(p + 17q + r) - (p + 7q + r) = 0
10q = 0
q = 0
Plug q = 0 into [1]:
p = -r
One of the vector is i + 0j - k
The unit vector
= {1/√[1² + (-1)²]} (i + 0j - k)
= (1/√2)i + 0j - (1/√2)k
2020-07-23 5:12 pm
Already asked and answered 3 days ago: https://answers.yahoo.com/question/index?qid=20200720095245AAgEkZh
2020-07-23 5:12 pm
(a × b) / |a × b|
This is a unit vector, and it is orthogonal to both a and b. I have not actually worked it out, but I do see that the first component is negative. Multiply it by -1, and all conditions will be satisfied.
-(a × b) / |a × b|
Equivalently: (b × a) / |b × a|
This is a unit vector, and it is orthogonal to both a and b. I have not actually worked it out, but I do see that the first component is negative. Multiply it by -1, and all conditions will be satisfied.
-(a × b) / |a × b|
Equivalently: (b × a) / |b × a|
收錄日期: 2021-04-24 07:54:03
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20200723084501AA0Wtaw