On the coordinate calculation of vector Given the vector a = (1-T, 1-T, t) and B = (2, t, t), then the minimum value of | B-A |?

On the coordinate calculation of vector Given the vector a = (1-T, 1-T, t) and B = (2, t, t), then the minimum value of | B-A |?

(1+t)2+(2t-1)2
This is a parabola. Let's find the lowest point by ourselves. I don't have any paper or pen

How to calculate the point multiplication of vector coordinates

For example, x = (A1, A2 ,an）
y=(b1,b2,… ,bn）
X dot multiplication y = A1 * B1 + A2 * B2 + +an*bn .

On the coordinate calculation of space vector
1 given that the angle between a (1,0,0), B (0, - 1,1), OA + λ OB and ob (o is the origin of coordinates) is 120 degrees, then the value of λ is - root 6 / 6, why root 6 / 6?

OA + λ ob = (1, - λ, λ), (OA + λ OB) dot times ob = 2 λ
And (OA + λ OB) dot multiplication ob = radical (2 λ ^ 2 + 1) * radical 2 * cos120 = - 0.5 * radical (4 λ ^ 2 + 2)
The two sides are equal: 4 λ = - radical (4 λ ^ 2 + 2), where λ must be negative, and the square of both sides is 16 λ ^ 2 = 4 λ ^ 2 + 2, so λ = - radical 6 / 6