AP EAPCET 23-Aug-2021 Shift 2 Paper

Since, we know that the direction ratio of line joining points (x1,y1,z1) and (x2,y2,z2) is <x2−x1,y2−y1,z2−z1>
Now, A=(4,1,2),B=(0,k,1)
∴ Direction ratio of line AB=<−4,k−1,−1>
Let a1=−4,b1=k−1,c1=−1
C=(−2,1,1),D=(4,2,5)
∴ Direction ratio of line CD=<6,1,4>
⇒a2=6,b2=1,c2=4
Given that, lines AB and CD are perpendicular to each other
⇒a1a2+b1b2+c1c2=0
⇒(−4)(6)+(k−1)(1)+(−1)(4)=0
⇒−24+k−1−4=0
⇒k=29