If the line joining A(4,1,2) and B(0, k, 1) is perpendicular to the line joining C(-2,1,1) and D(4,2,5) , then the value of k is equal to

Step-by-step solution

Since, we know that the direction ratio of line joining points (x₁, y₁, z₁ ) and (x₂, y₂, z₂ ) is Now, A=(4,1,2), B=(0, k, 1) Direction ratio of line A B= Let a₁=-4, b₁=k-1, c₁=-1C=(-2,1,1), D=(4,2,5) Direction ratio of line C D= a₂=6, b₂=1, c₂=4 Given that, lines A B and C D are perpendicular to each other array rrr & a₁ a₂+b₁ b₂+c₁ c₂=0 & (-4)(6)+(k-1)(1)+(-1)(4)=0 array -24+k-1-4=0 k=29