A vector problem Let I and j be two non collinear vectors, and the vectors AB = 3I + 2J, CB = I + λ J, CD = - 2I + J. if a, B and D are collinear, find the value of real number λ

A vector problem Let I and j be two non collinear vectors, and the vectors AB = 3I + 2J, CB = I + λ J, CD = - 2I + J. if a, B and D are collinear, find the value of real number λ

A. B, d three points collinear
AB//BD
BD=BC+CD=(-1-2)i+(-λ+1）j
-λ+1/-3=2/3
λ=3

Vector problems, solutions!
Given that | a | = 1, a * b = 1 / 2, (a-b) * (a + b) = 1 / 2, the angle between a + B and A-B is θ, then the value of cos θ is

(a+b).(a-b) =1/2
|a|^2-|b|^2=1/2
|b|^2 = 1/2
|a+b|^2= |a|^2+|b|^2+2a.b
= 1+ 1/2 + 1
= 5/2
|a+b| =√(5/2)
|a-b|^2= |a|^2+|b|^2-2a.b
= 1+ 1/2 - 1
= 1/2
|a+b| =1/√2
(a+b).(a-b) = |a+b||a-b|cosθ
1/2 = (√5/2) cosθ
cosθ = 1/√5