Let A(1,-1,2), B(6,11,2), C(1,2,6) be three points. If l₁, ~m ₁, n ₁ are the direction cosines of AB and l₂, ~m ₂, n ₂ are the direction cosines of AC , then |l₁ L₂+ m ₁ ~m ₂+ n ₁ n ₂ |=

Step-by-step solution

Direction ratios of A B are a₁=6-1=5, b₁=11-(-1)=12, c₁=2-2=0 Direction ratio's of A C are aligned & a₂=1-1=0, b₂=2-(-1)=3, c₂=6-2=4 & l₁= a₁ a₁^2+b₁^2+c₁^2 = 5 25+144+0 = 5 13 & m₁= b₁ a₁^2+b₁^2+c₁^2 = 12 25+144+0 = 12 13 & n₁= c₁ a₁^2+b₁^2+c₁^2 = 0 25+144+0 =0 & l₂= a₂ a₂^2+b₂^2+c₂^2 = 0 0+9+16 =0 & m₂= b₂ a₂^2+b₂^2+c₂^2 = 3 0+9+16 = 3 5 aligned aligned & n₂= c₂ a₂^2+b₂^2+c₂^2 = 4 0+9+16 = 4 5 & Then, |l₁ l₂+m₁ m₂+n₁ n₂ | & = | 5 13 0+ 12 13 3 5 +0 4 5 |= 36 65 aligned