The distance between parallel lines r =(2 i - j + k )+ (2 i + j - k ) and r =( i - j +2 k )+ (2 i + j -2 k ) is

Step-by-step solution

The distance between given parallel lines aligned & = | [( i -2 i )+(- j + j )+(2 k - k )] (2 i + j -2 k ) |2 i + j -2 k | |= | (- i + k ) (2 i + j -2 k ) (2)^2+(1)^2+(-2)^2 | & (- i + k ) (2 i + j -2 k )= | array ccc i & j & k -1 & 0 & 1 2 & 1 & -2 array |= i (0-1)- j (2-2)+ k (-1-0)=- i - k & d = | - i - k 9 |= 2 3 units aligned