If the lines x-2 1 = y-3 1 = z-4 -k and x-1 2 k = y-3 2 = z-5 1 are coplanar, then k can have

Step-by-step solution

The given lines are x-2 1 = y-3 1 = z-4 -k ...(i) and x-1 2 k = y-3 2 = z-5 1 ...(ii) Condition for two lines are coplanar | array ccc x₁-x₂ & y₁-y₂ & z₁-z₂ l₁ & m₁ & n₁ l₂ & m₂ & n₂ array |=0 where (x₁, y₁, z₁ ) and (x₂, y₂, z₂ ) are points on lines (i) and (ii) and ( .l₁, m₁, n₄ ) and (l₂, m₂, n₂ ) are direction cosines of lines (i) and (ii), respectively. aligned & | array ccc 2-1 & 3-3 & 4-5 1 & 1 & -k 2 k & 2 & 1 array |=0 & | array ccc 1 & 0 & -1 1 & 1 & -k 2 k & 2 & 1 array |=0 & 1(1+2 k)-0-1(2-2 k)=0 & 1+2