The point of intersection of the lines `l_(1) : r(t) = (i - 6j + 2k) + t(i + 2j + k), l_(2) : R(u) = (4j + k) + u(2i + j + 2k)` is

Find the shortest distance between the skew lines ⃗ r = ( ⃗ i + 2 ⃗ j + ⃗ k ) + λ ( ⃗ i − ⃗ j + ⃗ k ) and ⃗ r = ( 2 ⃗ i − ⃗ j − ⃗ k ) + η ( 2 ⃗ i + ⃗ j + 2 ⃗ k )

The angle between the planes r. (2i - j + 2k) = 3 and r. (3i - 6j + 2k) = 4

The line of intersection of the planes vec r . (3i-j+k) =1 and vec r . (i+4j-2k) = 2 is parallel to the vector

The lines r = i + j - k + lambda (3i - j) and r = 4i - k + mu (2i + 3k) intersect at the point