Given a (2,5, - 1), B (5,1,11), find the direction cosine and direction angle of AB vector,

Given a (2,5, - 1), B (5,1,11), find the direction cosine and direction angle of AB vector,

|A | = root sign (2 ^ 2 + 5 ^ 2 + (- 1) ^ 2) = root sign (30) | = root sign (5 ^ 2 + 1 ^ 2 + 11 ^ 2) = root sign (147) the directional cosine of AB vector is equal to the dot product of a and B divided by the product of their modules, that is: cos (a, b) = a · B / (| a | * | B |) = [2 * 5 + 5 * 1 + (- 1) * 11] / [root sign (30) * root sign (147)] = 2 * root sign (10) / 105

Given the direction vector, how to find the direction cosine?
For example: given the direction vector {1,4, - 8}, find the direction cosine {cos α, cos β, cos γ}

Direction cosine (x, y, z) of direction (x, y, z) / √ (x ^ 2 + y ^ 2 + Z ^ 2)
That is to say, we should unite it
So the directional cosine of {1,4, - 8) is (1,4, - 8) / 9

Two mathematical problems, there should be a process (√ is the root)
（1）√2（√2+2）
（2）√3（√3+1/√3）

(1)√2（√2+2）=2+2√2.
（2）√3（√3+1/√3）
=3+1
=4.