The shortest distance between the lines x-3 3 = y-8 -1 = z-3 1 and x+3 -3 = y+7 2 = z-6 4 is array ll a. 30 b. 2 30 & c. 5 _ x ( a² x²+b x+x -a x ) & = array

Step-by-step solution

L₁: x-3 3 = y-8 -1 = z-3 1 L₂: x+3 -3 = y+7 2 = z-6 4 Shortest distance between two lines = | | array ccc x₂-x₁ & y₂-y₁ & z₂-z₁ a₁ & b₁ & c₁ a₂ & b₂ & c₂ array | (b₁ c₂-b₂ c₁ )²+ (c₁ a₂-c₂ a₁ )²+ (a₁ b₂-a₂ b₁ )² | = | | array ccc -3-3 & -7-8 & 6-3 3 & -1 & 1 -3 & 2 & 4 array | (-4-2 )²+ (-3-12 )²+ (6-3 )² | = | | array ccc -6 & -15 & 3 3 & -1 & 1 -3 & 2 & 4 array | (-6)²+(-15)²+(3)² | On expanding the aligned &= 3(6-3)-1(-12-45)+4(6+45) 36+225+9 &= 9+57+204 270 = 270 270 = 270 =3 30 aligned