Name the pd between terminals of the cell when (i) key K is open (i) K is closed

If (1,2,4) and (2,-3 lambda , -3 ) are the initial and terminal points of the vector i+5j - 7k , then the value of lambda 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 )