​ If the shortest distance between the lines vector r1 = αi+2j+2k+λ(i - 2j+2k), λ ∈ R, α > 0 and vector r2 = -4i - k+μ(3i - 2j - 2k)

Question

If the shortest distance between the lines \(\overset{\rightarrow}{r_1}=\alpha\hat i+2\hat j+2\hat k\) \(+\lambda(\hat i-2\hat j+2\hat k)\), λ ∈ R, α > 0 and \(\overset{\rightarrow}{r_2}=-4\hat i-\hat k\) \(+\mu(3\hat i-2\hat j-2\hat k)\), μ ∈ R is 9, then α is equal to _________.

Answer 1

Answer is: 6

If \(\overset{\rightarrow}{r}=\overset{\rightarrow}{a}+\lambda\overset{\rightarrow}{b}\) and \(\overset{\rightarrow}{r}=\overset{\rightarrow}{c}+\lambda\overset{\rightarrow}{d}\)

then shortest distance between two lines is