The angle between the lines r =(2 i -3 j + k )+ ( i +4 j +3 k ) and r =( i - j +2 k )+ ( i +2 j -3 k ) is

Step-by-step solution

Given lines are and aligned & r =2 i -3 j + k + ( i +4 j +3 k ) & r =( i - j +2 k )+ ( i +2 j -3 k ) aligned Here DR's of given lines are (1,4,3) and (1,2,-3) . Angle between these lines is aligned & = a₁ a₂+b₁ b₂+c₁ c₂ a₁^2+b₁^2+c₁^2 a₂^2+b₂^2+c₂^2 & = 1 1+4 2+3 (-3) 1^2+4^2+3^2 1^2+2^2+(-3)^2 & = 1+8-9 1+16+9 1+4+9 =0 & = 2 aligned